Factor -1 out of the expression:
[tex]-1(3x^2-5x-2)[/tex]the coefficient of x² is 3 and the constant term is -2. The product of 3 and -2 is -6. The factors of -6 which sum to -5 are 1 and -6. Therefore:
[tex]undefined[/tex]Find the range of the function for the given domain. {-5, -1, 0, 2, 10}
[tex]g(x)=x^{2}+2[/tex]
A. 2
B. -23
C. 3
D. 1
E. 102
F. 27
G. 6
The range of the function g(x) = x² + 2 for the given domain is found to be {27,3,25,6,102}.
What is the difference between domain and range in function?The domain of a function is the set of values that may be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the collection of values that the function returns when we enter an x value.
How do you find domain and range in the absence of numbers?To determine the domain of a function, f(x), determine which values of x cause f(x) to be undefined/not real. The usual procedure for determining range is to find x in terms of f(x) and then locate values of f(x) for which x is not defined.
Given:
g(x) = x² + 2
Domain of the function: {-5, -1, 0, 2, 10}
We need to find the range.
Let us substitute x = -5 in g(x)
g(-5) = (-5)² + 2
= 27
g(-1) = (-1)² + 2
= 3
g(0) = (0)² +(-5)²
= 25
g(2) = (2)² + 2
=6
g(10) = (10)² + 2
= 102
Therefore, the range of the given function g(x) = x² + 2 for a given domain is found to be {27,3,25,6,102}.
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In the items below a physical property is identified along with two objects/figures. For each item identity whether the property applies to one, both, or neither of the objects/figures listed and explain why it does or does not.1) Property: MassCylinder Square
Background
• Mass: ,is the quantity of matter in a physical body.
,• Cylinder: ,a three-dimensional solid.
,• Square: ,a one-dimensional figure (flat shape).
As a square is just a one-dimensional figure, it cannot have mass, then...
Answer: the property applies only to the Cylinder.
can someone help me set it up im very confused.
let h be the height of the television set
4: 3 = 46 : h
[tex]\frac{4}{3}=\frac{46}{h}[/tex]cross multiply
4h = 138
Divide both-side of the equation by 4
h = 34.8 inches
Diego's goal is to walk more than 70,000 steps this week. The mean number of steps that Diego walked during the first 4 days of the week is 8,019.If the mean number of steps Diego walks during the last 3 days of the week is 12, 642, will Diego reach his goal of walking more than 70,000 steps this week? Explain your reasoning.
Solution
Diego goal was walk more than 70000 steoes
And in average in the first 4 days he walks 8019 steps
The expected mean number of steps for the next 3 days is 12642 then we can do this:
8019*4 + 12642*3= 32076 +37926 = 70002
then since 70002 > 70000
We can conclude that Diego can reach the goal for this case
For each value of v, determine whether it is a solution to v - 42 = 11
Given equation:
[tex]v\text{ - 42 = 11}[/tex]The first step is to solve the equation i.e. find the value of v
[tex]\begin{gathered} Collect\text{ like terms} \\ v\text{ = 11 + 42} \\ v\text{ = 53} \end{gathered}[/tex]The given options
What is the value of x?2445°X=(Simplify your answer. Type an exact answer, using radicals as needed.)
Given the figure of a right-angle triangle
As shown, the given triangle is a 45-45-90 triangle
The relation between the hypotenuse (h) and the length of one leg (l) is as follows:
[tex]h=(\sqrt{2})l[/tex]As shown, h = 24, and l = x
[tex]\begin{gathered} 24=\sqrt{2}*x \\ \\ x=\frac{24}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{24\sqrt{2}}{2}=12\sqrt{2} \end{gathered}[/tex]So, the answer will be:
[tex]x=12\sqrt{2}[/tex]Find the equation of the line in standard form that passes through the following points simplify your answer
Given: Two points
[tex]\begin{gathered} Point1:(10,11) \\ Point2:(10,7) \end{gathered}[/tex][tex]\begin{gathered} Point1:(10,11) \\ Point2:(10,7) \end{gathered}[/tex]To Determine: The equation of the line in standard form that passes through the given points
Solution
The equation of a line passing through two different points is given as
[tex]\begin{gathered} Point1:(x_1,y_1) \\ Point2:(x_2,y_2) \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Substitte the given coordinates of the points given into the formula
[tex]\begin{gathered} \frac{y-11}{x-10}=\frac{7-11}{10-10} \\ \frac{y-11}{x-10}=\frac{-4}{0} \\ cross-multiply \\ Since\text{ the slope is undefine} \\ The\text{ equation of the line is } \\ x=10 \end{gathered}[/tex]The standard form of a line is given as
[tex]Ax+By=C[/tex]But since the x-coordinates of the points are equal, then the formula for slope is not applicable (the denominator equals 0).
In this case, we say that the slope is undefined (the line is vertical).
This means that the equation of the line doesn't contain y.
Thus, the equation of the line is x=10.
Answer: the slope is undefined.
The equation of the line is x = 10.
write a multiplication equation for the area of the square with side lengths of 1 meter
Area of a square is expressed using the formula;
A = L^2
L is the side length of the square
From the question, we are given;
L = 1 meter
The multiplication equation for the area of the square will be;
A = 1 meter * 1 meter
A = 1m^2
At a certain hospital 39080 patients had their falls reported in the winter of 2004, thisrose to 42045 patients in the winter of 2014 (Lifespan, 2019). How would you calculatethe percentage rise in patients from 2004 to 2014?In a several sentences, how would you apply this to your life or job? If you had to teachsomeone who did not know how to this, what would be the steps from beginning to endthat you would use to teach them so that they would eventually do it accurately as youwould?Professor,I would calculate the percentage rise in patients from 2004 to 2014 by
Percentage rise in patients from 2004 to 2014 = 7.59%
Explanation:The number of patients in 2004 = 39080
The number of patients in 2014 = 42045
Increase in the number of patients = (The number of patients in 2014) - (The number of patients in 2004)
Rise in the number of patients = 42045 - 39080
Rise in the number of patients = 2965
[tex]\begin{gathered} \text{Percentage rise in patients = }\frac{\text{Rise in the number of patients}}{\text{Number of patients in 2004}}\times100 \\ Percentage\text{ rise in patients = }\frac{2965}{39080}\times100 \\ \text{Percentage rise in patients = }7.59\text{ \%} \end{gathered}[/tex]Percentage rise in patients from 2004 to 2014 = 7.59%
Solve this equation:-36q = 18
Given:
[tex]36q=18[/tex]Required:
To solve the given equation.
Explanation:
Consider
[tex]36q=18[/tex]Divide 36 on both side, we get
[tex]\begin{gathered} \frac{36q}{36}=\frac{18}{36} \\ \\ q=\frac{18}{36} \\ \\ q=\frac{1}{2} \end{gathered}[/tex]Final Answer:
[tex]q=\frac{1}{2}[/tex]60 is what % of 150? Can you help?
Given:
There are given that the final number is 150.
Explanation:
According to the question:
We need to find the percentage number.
Then,
Suppose the percentage number is x.
Then,
The equation will be:
[tex]150\times x\%=60[/tex]Now,
We need to solve the above equation for the value of x.
Then,
Divide by 150 on both sides of the equation:
[tex]\frac{150}{150}\times x\operatorname{\%}=\frac{60}{150}[/tex]Then,
[tex]\begin{gathered} x\%=\frac{60}{150} \\ x\operatorname{\%}=\frac{6}{15} \\ x\operatorname{\%}=0.4 \\ x=0.4\times100 \\ x=40 \end{gathered}[/tex]Final answer:
Hence, the percentage is 40%.
perimeter of a square must be greater than 118 inches but less than 156 inches .find the range of the possible side lengths that satisfy these conditions . formula p= 4sput answer in interval notation.
the perimeter of a square must be greater than 118 inches but less than 156 inches.
Perimeter = 4 side lenght
P = 4 s
118 < 4s < 156
Divide by 4
29.5 < s < 39
(29.5 , 39 )
Jack has an old scooter. He wants to sell it for 60% off the current price. The
market price is $130. What should his asking price be? Explain your reasoning.
determine the length of the unknown side of the right angle
We are given the right-angle triangle with two known sides and one unknown side.
We can use the Pythagoras theorem to find the length of the unknown side.
Recall that Pythagoras theorem is given by
[tex]a^2+b^2=c^2[/tex]Where c is the side opposite to the 90° angle.
Let us substitute the given values into the above equation
[tex]a^2+(9)^2=(15)^2[/tex]Simplify the equation
[tex]\begin{gathered} a^2+81=225^{} \\ a^2=225-81 \\ a^2=144 \end{gathered}[/tex]Take the square root on both sides
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{144} \\ a=12 \end{gathered}[/tex]Therefore, the length of the third side of the right angle tri
marh questions i need to solve and i have problems with it
7.
Given the side ratio as:
[tex]5:13[/tex]The area ratio is the second power of the above, which is:
[tex]\begin{gathered} 5^2:13^2 \\ =25:169 \end{gathered}[/tex]Given the area ratio of:
[tex]36:49[/tex]The perimeter ratio is:
[tex]\begin{gathered} \sqrt{36}:\sqrt{49} \\ \\ =6:7 \end{gathered}[/tex]On Monday, Freda spent $20 to buy 3 burgers and 4 orders of fries for her friends to share for lunch. Let r represent the cost of a burger and y represent the cost of an order of fries. What linear equation would model this?
Let:
r = Cost of a burger
y = Cost of an order of fries
Freda spent $20 to buy 3 burgers and 4 orders of fries for her friends to share for lunch, therefore:
[tex]3r+4y=20[/tex]A mattress with a list price of $2300 will be discounted 30% at the time of purchase. What is the sale price before taxes?
So,
30% of $2300 is:
[tex]\frac{30\cdot2300}{100}=690[/tex]So that's the amount that will be discounted. Therefore, the sale price before taxes is $2300 - $690 = $1610
Consider the equation. y=1/4(x-5)^2-3Vertex (5,-3)The next step in graphing a parabola is to find points that will determine the shape of the curve. Find the point on the graph of this parabola that has the X-coordinates X=3.
We have the equation:
[tex]y=\frac{1}{4}(x-5)^2-3[/tex]This is a parabola expressed in vertex form, where the vertex is (h,k) = (5,-3).
We have to graph the parabola. To do that we need another point, as we already know the vertex and, therefore, the axis of symmetry (x = 5).
We can find another point by giving a value to x and calculating y.
For example, with x = 3 we get:
[tex]\begin{gathered} y(3)=\frac{1}{4}(3-5)^2-3 \\ y(3)=\frac{1}{4}(-2)^2-3 \\ y(3)=\frac{1}{4}\cdot4-3 \\ y(3)=1-3 \\ y(3)=-2 \end{gathered}[/tex]The point that belongs to the parabola when x = 3 is (3, -2).
Then, we can graph the two points and draw the parabola as:
Because of the symmetry at x = 5, we also know that two units to the right, at x = 7, we will have the same value of y that we have for x = 3.
With at least 3 points, we can graph a parabola.
The actual graph is:
If we want to add more precision to our graph, we can calculate more points that belong to the parabola.
For example, at the other side of the vertex, we can calculate the value of y for x = 6:
[tex]\begin{gathered} y(6)=\frac{1}{4}(6-5)^2-3 \\ y(6)=\frac{1}{4}(1)^2-3^{} \\ y(6)=\frac{1}{4}-3 \\ y(6)=\frac{1}{4}-\frac{12}{4}^{} \\ y(6)=-\frac{11}{4}=-2.75 \end{gathered}[/tex]We can add this to the plot as:
We have to aproximate the position of y as the grid only shows integers and y = -2.75.
Answer:
The points in the parabola are (5,-3), (3,-2) and (6,-2.75). We need at least 3 points to plot a parabola.
Hello can you assist me with number 11Find the midpoint
Answer:
(-3, 2.5)
Explanation:
The midpoint of two points of coordinates (x1, y1) and (x2, y2) has the following coordinates
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}_{})[/tex]Then, the midpoint can be calculated replacing (x1, y1) = (3, 3) and (x2, y2) = (-9, 2), so
[tex](\frac{3+(-9)}{2},\frac{3+2}{2})=(\frac{-6}{2},\frac{5}{2})=(-3,2.5)[/tex]Therefore, the midpoint is (-3, 2.5)
13. What transformations take place by graphing the function below in respect to its parents go
function? Check all that apply.
Up 7 units
Down 7 units
Left 7 units
Right 7 units
3
f(x)=(x+7)² +2
Up 2 units
Down 2 units
Left 2 units
Right 2 units
Theis)
Textes
Vertical Stretch
Vertical Compression
Reflection in x-axis
Reflection in y-axis
81
The graph is being transformed Right 7 units and Down 2 units.
The function is given as:
f (x) = (x + 7)² + 2
This can also be written as:
y = (x + 7)² + 2
y - 2 = (x + 7)²
Now, we can see the following transformations:
The graph is translated 7 units to the right.
Also, it is being translated 2 units to the down.
So, the option will be
Right 7 units and Down 2 units
Therefore, we get that, the graph is being transformed Right 7 units and Down 2 units.
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If D is the midpoint of AB and AD = 2x + 6 and AB = 32, then find AD. Draw thepicture.AD =
The diagram representing the line AB and midpoint D is shown bel;ow.
Therefore, 16=2x+6.
[tex]\begin{gathered} 2x=10 \\ x=5 \end{gathered}[/tex]Then, the magnitude of AD will be,
[tex]\begin{gathered} AD=(2\times5)+6 \\ AD=16 \end{gathered}[/tex]Therefore, the answer is 16.
A company is going to make a storage container with sheet steel walls. The container will be in the shape of a rectangular prism, as shown below. If the sheet steel costs $30 for each square meter, how much will the sheet steel cost in total?
ANSWER
$3060
EXPLANATION
Each steel sheet used for the prism costs $30 per square meter.
To find the total cost of the sheet, we have to find the surface area of the rectangular prism. Then we multiply the surface area by the cost per square meter.
The surface area of a rectangular prism is:
[tex]\begin{gathered} A\text{ = 2(}wh\text{ + wl + hl)} \\ \text{where h = height} \\ w\text{ = width} \\ l\text{ = length} \end{gathered}[/tex]From the diagram:
l = 7 m ; w = 3 m ; height = 3 m
Therefore, the surface area of the prism is:
[tex]\begin{gathered} A\text{ = 2\lbrack(3 }\cdot\text{ 3) + (3 }\cdot\text{ 7) + (3 }\cdot\text{ 7)\rbrack} \\ A\text{ = 2(9 + 21 + 21)} \\ A\text{ = 2(51)} \\ A\text{ = 102 square meters} \end{gathered}[/tex]Now, we multiply by the cost per square meter:
[tex]\begin{gathered} C\text{ = 102 }\cdot\text{ 30} \\ C\text{ = \$3060} \end{gathered}[/tex]That is the total cost of the steel sheet.
The ages (in years) of the 5 doctors at a local clinic are the following30, 40, 39, 36, 30Assuming that these ages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places
Solution
For this case we have the following data:
30, 40, 39, 36, 30
Representing the ages (in years) of the 5 doctors at a local clinic
these values represent an entire population, and we want to find the standard deviation of the population
1) First we need to calculate the mean
[tex]\mu=\frac{30+40+39+36+30}{5}=35[/tex]2) Now we can find the population variance like this:
[tex]\sigma^2=\frac{(30-35)^2+(40-35)^2+(39-35)^2+(36-35)^2+(30-35)^2}{5}=\frac{92}{5}=18.4[/tex]3) Calculate the population standard deviation
[tex]\sigma=\sqrt[]{18.4}=4.29[/tex]then the answer would be:
4.29
Jeremy says this dilation can be represented by (X+3\4,Y+3\4)Julie says this dilation can be represented by (3\4X, 3\4Y)whoo is correct and why
The scale factor for dilation is 3/4. Therefore, the dilation can be represented below
[tex](\frac{3}{4}x,\frac{3}{4}y)[/tex]This means Julie is correct.
What is the slope of the line that passes through the points (10,8) and (7,14)?
Answer:
Step-by-step explanation:
-0.5
6ft 3ft 8ft 16ft area of irregular figures
Solution.
From the figure given we will have to find the
(Area of A) + (The Area of B)
STEP 1 :
For figure B
b = 3
h = 6
[tex]\begin{gathered} \text{Area of A = }\frac{1}{2}\times b\times h \\ \text{ = }\frac{1}{2}\times3\times6 \\ \text{ = }\frac{18}{2}\text{ = 9} \end{gathered}[/tex]Step 2:
For Figure A
L = 16
b = 8ft
Area of B = L x B
= 16 x 8
= 128
STEP 3
Area of A + Area of B
128 + 9 = 137 square feet
Yusuf is going to the amusement park, where he has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money Yusuf will spend is given by the equation y=4x+20y=4x+20, where yy represents the total amount of money, in dollars and cents, and xx represents the number of rides Yusuf goes on. What could the number 20 represent in the equation?A.The total amount of money Yusuf will spend if he goes on 1 ride.B.How much it cost for a ticket to go on one of the rides.C.The total amount of money Yusuf will spend if he goes on 0 rides.DThe total amount of money Yusuf will spend if he goes on 100 rides.
Given the equation:
[tex]y=4x+20[/tex]If x = 0, then:
[tex]\begin{gathered} y=4\cdot0+20 \\ \Rightarrow y=20 \end{gathered}[/tex]Answer: C
y=1/2x what is the b, or y-intercept in this equation
The given equation is
[tex]y=\frac{1}{2}x[/tex]The slope-intercept form is
[tex]y=mx+b[/tex]The given equation can be written as follows.
[tex]y=\frac{1}{2}x+0[/tex]Comparing this equation with slope-intercept form, we get b=0.
Hence the value of b or y-intercept in the given equation is 0.
Translate the following word phrase to an algebraic expression and simplify: “8 times the difference of 6 times a number and 3”
Given the word phrase
8 times the difference of 6 times a number and 3
Let the number = x
6 times the number = 6x
The difference of 6 times the number and 3 = 6x - 3
8 times the difference of 6 times a number and 3 will be:
[tex]8(6x-3)[/tex]Convert the measurement as indicated 83 qt = Gal Qt
20 gallons 3 quarts
Explanation:Note that:
1 quart = 0.25 gallons
83 quarts can be written as
80 quarts + 3 quarts
80 quarts = 80 x 0.25 gallons
80 quarts = 20 gallons
Therefore:
83 quarts = 20 gallons 3 quarts