P(x) = P(-2)
P(-2) = 3(-2)^2 + 5(-2)-8
= 3(4) + (-10) - 8
= 12 + (-10 -8)
= 12 + (-18)
= 12 - 18
= - 6
P(-2) = -6
(divided on both sides by -2)
Answer:
P = 3
(btw i am not sure if this is the answer you are looking for. Please clarify ths objective of this equation. What are we looking for? Are we solving for "P" ?)
A plumber charges $85 to start a job plus $46 per hour. If the plumber charges his customer based on every half hour, how many hours can Fred afford to have the plumber work if he only has $250?
The maximum number of hours he can afford is 3 hours
Here, we want to get the number of hours Fred can afford to have the plumber work
From the question, we have a fixed $85 charge
Let the number of hours worked be h
Thus, we have an equation where the cost of hiring is c
We have this as;
[tex]c\text{ = 46h+85}[/tex]Now, from the question, we are told that the charge is based on every half-hour
We can now have;
[tex]\begin{gathered} 250\text{ = 46h+85} \\ 250-85\text{ = 46h} \\ 46h\text{ = 165} \\ h\text{= }\frac{165}{46} \\ h\text{ =}3.5 \end{gathered}[/tex]Tell whether the function shown by the table is linear or nonlinear.
HELP ME PLEASE
PLEASE HELP
The function shown by the table is linear function
How to categorize the function on the table?From the question, we have the following parameters that can be used in our computation:
The table
On the table of values, we can see that:
The table is divided into two columns
The x and the y columns
On the x column, we can see that the x values have a common difference of 1On the y column, we can see that the y values have a common difference of 6.5Because both columns have common differences, then the table is a linear function
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What is 3 1/5 * 2 1/4
To multiply two mixed numbers, one way to do it is to convert them into pure fractions and then multiply them:
[tex]3\text{ 1/5}\cdot2\text{ 1/4}=(3+\frac{1}{5})\cdot(2+\frac{1}{4})=(\frac{15+1}{5})\cdot(\frac{8+1}{4})=\frac{16}{5}\cdot\frac{9}{4}=\frac{144}{20}=\frac{36}{5}[/tex]The product is 36/5, that can be expressed as mixed number as:
[tex]\frac{36}{5}=\frac{35+1}{5}=7+\frac{1}{5}[/tex]Answer: The product (3 1/5 * 2 1/4) is 36/5 or 7 1/5.
help meeeeeeeeeeeeeeee pleasee
If the height of the triangle is three more than four times its base, then the base of the triangle is x units and height of the triangle is 4x+3 units
The base of the triangle = x units
The height of the triangle is three more than four times its base
Four times the base = 4 × x
= 4x
Three more than four times its base = 4x+3
The height of the triangle is three more than four times its base
The height = 4x+3 units
Hence, If the height of the triangle is three more than four times its base, then the base of the triangle is x units and height of the triangle is 4x+3 units
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6 Q Find the area of the circle pictured above. Round your answer to the nearest tenth
Answer:
28.3 units^2
Explanation:
The area A of the circle is given by the formula
[tex]A=\pi(\frac{d}{2})^2[/tex]where
π = 3.1415..
d = diameter of the circle.
Now, in our case d = 6; therefore,
[tex]A=\pi(\frac{6}{2})^2[/tex][tex]A=(3.1415)(3)^2[/tex][tex]A=(3.1415)(9)[/tex][tex]A=28.274[/tex]Rounded to the nearest tenth this is
[tex]A=28.3[/tex]please help ASAP!!!!!
Solution
For this case we can begin dividing both sides by 3500 and we got:
[tex]\frac{3992}{3500}=(1+r)^2[/tex]then we can take square root in both sides and we got:
[tex]\sqrt[]{\frac{3992}{3500}}=1+r[/tex]And finally we can subtract 1 in both sides and we got:
[tex]r=\sqrt[]{\frac{3992}{3500}}-1=0.06797[/tex]and if we multiply by 100 we got:
r= 6.797 and rounded the answer would be:
6.8%
What is the ratio for the volumes of two similar cylinders, given that the ratio of their heights and radii is 2:3?
It's important to know that volumes are three-dimensional magnitudes, which means they are cubic powers. In this case, we just have to elevate the given ratio to the third power.
[tex](\frac{2}{3})^3=\frac{8}{27}[/tex]Hence, the answer is A.Q14
Marco has a 4-sided spinner. The sides of the spinner are numbered 1, 2, 3 and 4. The spinner is biased.
The table shows the probability that the spinner will land on each of the numbers 1, 2 and 3. 4 Number Probability 1 0.20 2 0.35 3 0.20
(a) Work out the probability that the spinner will land on the number 4. Marco spins the spinner 100 times.
(b) Work out an estimate for the number of times the spinner will land on the number 2.
Answer:
1. 0.25
2. 35
Step-by-step explanation:
1. Total probability of all outcomes put together should be 1. So,
P(4) = 1 - ( P(1) + P(2) + P(3) )
= 1 - ( 0.2 + 0.35 + 0.2 )
= 0.25
2. If probability for 2 to come up is 0.35, then expected number of 2 after 100 spins will be 100*0.35 = 35.
a 20-acre Orchard is planted with apple and peach trees at most $10,000 going to be spent on planting cost planting cost for apple trees $400 per acre in for peach trees $1,000 per acre choose the best graph that shows the area of each crop that can be planted
According to the equation x + y ≤ 20, graph (D) best represents the area of each crop that can be planted.
What is a graph?The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and connecting lines. It doesn't matter how long the lines are or where the points are located. A node is a name for each element in a graph.Charts and graphs come in a variety of styles. Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types.
So, let the number of acres for apple trees be = x.
The number of users for the peach tree is = y.Then according to the question:
400x + 1000y ≤ 10000x + y ≤ 20(Refer to the graph as answered marked below)
The fourth graph is the best graph that shows the area of each crop that can be planted.Therefore, according to the equation x + y ≤ 20, graph (D), best represents the area of each crop that can be planted.
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Let f(x) = Võ - 6 and g(x) = x2 + 5.(fog)(x) =.(gof)(x) =
Recall the following:
[tex]\begin{gathered} (f\circ g)(x)=f(g(x)), \\ (g\circ f)(x)=g(f(x)). \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} (f\circ g)(x)=f(x^2+5)=\sqrt[]{(x^2+5)}-6, \\ (g\circ f)(x)=g(\sqrt[]{x}-6)=(\sqrt[]{x}-6)^2+5. \end{gathered}[/tex]Answer:
Simplifying the above equations we get:
[tex]\begin{gathered} (f\circ g)(x)=\sqrt[]{x^2+5}-6, \\ (g\circ f)(x)=(\sqrt[]{x}-6)^2+5=x-12\sqrt[]{x}+36+5=x-12\sqrt[]{x}+41, \\ (g\circ f)(x)=x-12\sqrt[]{x}+41. \end{gathered}[/tex]Write the equation of this function in the form y=x+b X 0 4 12 у 6 10 18
Step1: Pick 2 points in the table:
(0,6) and (4,10)
Step2: Recall the formula for the slope of a line.
[tex]\text{Slope =}\frac{y_2-y_1}{x_2-x_1}[/tex]Step3: Substitute the values of the coordinates in the above formula.
[tex]\begin{gathered} (0,6)\Rightarrow x_1=0;y_1=6 \\ (4,10)\Rightarrow x_2=4;y_2=10 \end{gathered}[/tex]Step4:
[tex]\text{Slope =}\frac{10-6}{4-0}=\frac{4}{4}=1[/tex]Step5: Invoke the formula for the equation of the line.
[tex]\begin{gathered} y-y_1=slope(x-x_1) \\ y-6=1(x-0) \\ y-6=x \\ y=x+6 \end{gathered}[/tex]Hence, the correct answer is y = x + 6
Select the correct answer from each drop-down menu.The function f is given by this table of values.х-10Use this table to complete the statements.The parent function of the function represented in the table isIf function fis vertically compressed by a factor of , the-values will beA point in the table for the transformed function is
As we can note the tables shows a linear behavior. Then, the parent function of the function represented in the table is linear.
If function f is vertically compressed by a factor of 1/4, the f(x) - values will be divided by 4.
Form a polynomial whose real zeros and degree are given.Zeros: -3, - 1,3,5;degree: 4Type a polynomial with integer coefficients and a leading coefficient of 1.f(x)=(Simplify your answer.)=
Given:
a.) Zeros: -3, -1, 3, 5
b.)Degree: 4
Determine the equation of the line that passes through the (8,-27) and is parallel to the line y = - 3x - 1
The equation parallel to the given equation, and passing through the given point is
y = -3x - 3
Explanation:Given the line:
y = -3x - 1 ................................................(1)
The slope of this equation is -3
A line parallel to this line has the same slope as this, but a different y-intercept.
Let the parallel line be
y = -3x + b ..............................................(2)
To find the unknown b, we use the given point (8, -27), i.e x = 8, y = -27 into equation (2) and solve for b
-27 = -3(8) + b
-27 = -24 + b
b = -27 + 24
= -3
Substitute the value of b into (2), we have
y = -3x - 3
Writing The diameter of Circle J is 18 cm. The diameter of Circle K is 31 cm. Which circle has thegreater area and by how much? Use 3.14 for r. Use pencil and paper. Describe two ways you cancompare the areas of two circles. Explain when you might prefer to use each.Select the correct choice below and fill in the answer box to complete your choice.(Round to the nearest whole number as needed.)O A. The area of Circle K is about cm2 greater than the area of Circle J.OB. The area of Circle J is about cm2 greater than the area of Circle K.
ANSWER :
A. The area of Circle K is about 500 cm^2 greater than the area of Circle J.
EXPLANATION :
Recall the area formula of a circle :
[tex]A=\pi r^2[/tex]Note that the radius is half of diameter.
The diameter of Circle J is 18 cm so the radius is 18/2 = 9 cm
The diameter of Circle K is 31 cm so the radius is 31/2 = 15.5 cm
The areas are :
[tex]\begin{gathered} \text{ Circle J :} \\ A=(3.14)(9)^2=254.34cm^2 \\ \text{ Circle K :} \\ A=(3.14)(15.5)^2=754.385cm^2 \end{gathered}[/tex]The area of Circle K is greater than Circle J by 754.385 - 254.34 = 500.045 cm^2 or 500 cm^2
Problem b (4.0 x 10^2)(4.0 x 10^7)Problem c (7.0 x 10^-3)(6.0 x 10^6)Problem d (1.2 x 10^7)(2.2 x 10^-3)Problem e (2.0 x 10^-4)(7.1 x 10^9)
Answer;
[tex]16\times10^9[/tex]Explanation:
Here, we want to get the product of the given expression
Since the base are the same,, we use the indices rule which is:
[tex]\text{ (a}^x)\text{ }\times(a^y)=a^{x\text{ + y}}[/tex]We apply that in this same problem as follows:
[tex]\begin{gathered} \text{ 4.0}\times\text{ 4.0}\times10^2\times10^7 \\ =4.0^2\times10^{2+7} \\ =\text{ 16}\times10^9 \end{gathered}[/tex]The angle of elevation from a ship to the top of a cliff on the coastline is 4.5°. The cliff is 375 feet in height. How far is the ship from the base of the cliff? Round to the nearest tenth.
Solution:
The given information would be illustrated with the image below as;
We would apply the tangent ratio. Let x be the distance between the base of cliff and the ship. We have;
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \tan 4.5^o=\frac{375}{x} \\ \\ \end{gathered}[/tex]Then, we have;
[tex]\begin{gathered} x=\frac{375}{\tan4.5^o} \\ x=4764.8ft \end{gathered}[/tex]FINAL ANSWER:
[tex]4764.8\text{feet}[/tex]Solve for the value of x that would make line 1 parallel to line m.
From the diagram, we can see that line l is parallel to m. Taking the angle (3x-18) on line m to line l, we will see that both 105 and (3x-18) are adjacent to each other and lies on the same striaght line l.
Since sum of angle on a straigth line is 180, hence;
105 + 3x-18 = 180
3x + 105 - 18 = 180
3x + 87 = 180
Subtract 87 from both sides;
3x+87-87 = 180-87
3x = 93
x = 93/3
x = 31
Hence the value of x is 31 degrees
At the beginning of spring, Eva planted a small sunflower in her backyard. When it was first planted, the sunflower was 15 inches tall. The sunflower then began to grow at a rate of 1 inch per week. How tall would the sunflower be after 8 weeks? How tall would the sunflower be after ww weeks?
The height of the sunflower after 8 weeks will be 23 inch and after w weeks it will be (15+w) inches tall .
In the question ,
it is given that
when the sunflower was planted
the height was 15 inches .
and the flower grows by 1 inch every week ,
So , in 8 weeks the flower will grow = 8*1 = 8 inches
and in w weeks the flower will grow = w inches
So, the height of the flower plant after 8 week = 15 + 8 = 23 inches
and the height of the flower plant after w weeks is = (15+w) inches
Therefore, The height of the sunflower after 8 weeks will be 23 inch and after w weeks it will be (15+w) inches tall .
The given question is incomplete , the complete question is
At the beginning of spring, Eva planted a small sunflower in her backyard. When it was first planted, the sunflower was 15 inches tall. The sunflower then began to grow at a rate of 1 inch per week. How tall would the sunflower be after 8 weeks? How tall would the sunflower be after w weeks?
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This is a two-part questionDave wants to buy a new collar for each of his three cats. The collars come in a choice of five different colors.How many selections of collars for the three cats are possible if repetitions of colors are allowed.Part 2: How many selections of collars are possible if repetitions of colors are not allowed
1) Notice that there are three cats, and each collar has 5 options (colors).
2) Based on that, we can write the following, considering the repetitions of colors are allowed.
Thus, there are 125 possibilities (selections) for picking colors for this set of three collars.
Part 2) Given that now, it is not allowed repetitions we can use the same diagram with a little adjustment: the number of possibilities over the dash is going to be decreasing for each picking means one less option.
Since Dave cannot repeat any color, there are now 60 selections to be made.
Connie makes handmade quilts for her grandchildren each quilt is 4ft by 6ft what is the approximate length of the diagonal of the quilt
Connie makes handmade quilts for her grandchildren each quilt is 4ft by 6ft what is the approximate length of the diagonal of the quilt
Applying the Pythagorean Theorem
Let
x -----> the diagonal of the quilt
x^2=4^2+6^2
x^2=16+36
x^2=52
x=7.21 ft
therefore
the approximate length of the diagonal is 7 ft
A house cost $185,500 in 2000. By the year 2015 the value was $132,000. What was the growth rate as a percentage for that 15-year period. (Remember, i=(P1/P1) 1/n-1)
Let's begin by listing out the information given to us:
Cost, Year 2000 (Old price) = $185,500
Cost, Year 2015 (New price) = $132,000
Year difference = 15 years
The growth rate is calculated as:
[tex]\begin{gathered} i=(\frac{p_2}{p_1})^{\frac{1}{n}}-1 \\ i=(\frac{132000}{185500})^{\frac{1}{15}}-1 \\ i=0.97757-1=-0.0224 \\ i=-0.0224\cdot100\text{\%}=-2.24\text{\%} \\ i=-2.24\text{\%} \end{gathered}[/tex]use the propertied of exponents to simplify the expression (-36)^0
That is the proporty of the zero exponent.
Every number that has a zero exponent will be equal to 1.
So,
[tex]\text{ (-36)}^0\text{ = 1}[/tex](-1 05 4i need help
answer:
Dimensions of the matrix 1: 2 x 2
dimensions of the matrix 2: 1 x 2
To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix, therefore the answer is
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im trying to see if what i think the answer is is correct for the width i got 2x^2+1
Given the expression:
[tex]10x^2+5x[/tex]we already know that 5x is a common factor, then, if we divide each term by 5x we get:
[tex]\begin{gathered} \frac{10x^2}{5x}=2x \\ \frac{5x}{5x}=1 \end{gathered}[/tex]then, we can factor the expression like this:
[tex]10x^2+5x=5x(2x+1)[/tex]therefore, the width of Heng's area model is 2x+1
Triangles A and B are similar. The side lengths of Triangle A in inches are 4.5, 7.0, and 5.25. The corresponding lengths in inches for Triangle B are 13.5, 21.0, and x. Solve for x.
Answer:
The value of x is 15.75
Explanation:
Given that triangles A and B are similar.
Side lengths of triangle A are: 4.5, 7.0, and 5.25
Side lengths of triangle B are: 13.5, 21.0, and x
Since the triangles are similar, the following ratios are correct:
13.5/4.5 = 21/7 = x/5.25
3 = x/5.25
Multiply both sides of the equation by 5.25
x = 15.75
When you throw a penny and a nickel what is the probability of both the coins landing tails
1) Let's enlist all the possible outcomes. H-Heads, T-tails. If we toss two coins penny and a nickel then we would have:
(t,t) (h,t) (t,h) and (h,h) 4 total outcomes
2) Since we want to know the chance of getting tails, then we'll call tails our favorable outcome. From the total outcomes, we can count that there is only one possibility:
(t,t) (h,t) (t,h) and (h,h) 1 favorable outcome
(t,t) so we can write:
[tex]P(tails)=\frac{1}{4}[/tex]Thus, this is the answer 1/4
Determine the values of m in the equation m2 = 25.
Answer:positive or negative 5
Step-by-step explanation:
Answer: +5
Step-by-step explanation:
did the quiz and got it correct
What is the whole number 26 as a fraction in simplest terms?
The whole number 26 as a fraction in its simplest form is 26/1.
Whenever we have a whole number and we have to represent it as a fraction, we can write them as whole number/ 1.
It is because any number divided by the 1 is the same number.
Hence, the whole number 26 can be represented as 26/1 in a fractional form.
Fraction
Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator and the number on the bottom of the line is called denominator.
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Which ratio isn't equivalent to the others? a 2:1 b 9:3c 8:4d 10:5
Answer:
b. 9:3
Explanation:
To determine the equivalent ratios. reduce each to its lowest form:
[tex]\begin{gathered} 2\colon1=2\colon1 \\ 9\colon3=3\colon1 \\ 8\colon4=2\colon1 \\ 10\colon5=2\colon1 \end{gathered}[/tex]Thus, the ratio that is not equivalent is 9:3.