Ans expression based
(a) f(2) − f(−2) = −4.5
(b) f(−1)f(−2) = 18
(c) −2f(−1) = −12
(a) To evaluate f(2) − f(−2), we need to first find the value of f(2) and f(−2). From the table, we see that f(2) = −1.5 and f(−2) = 3. Therefore,
f(2) − f(−2) = −1.5 − 3 = −4.5
(b) To evaluate f(−1)f(−2), we simply need to multiply the values of f(−1) and f(−2). From the table, we see that f(−1) = 6 and f(−2) = 3. Therefore,
f(−1)f(−2) = 6 × 3 = 18
(c) To evaluate −2f(−1), we simply need to multiply the value of f(−1) by −2. From the table, we see that f(−1) = 6. Therefore,
−2f(−1) = −2 × 6 = −12
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If you can please explain how you got your answer so I can understand, Thank you!
Answer:
3 2/5
Step-by-step explanation:
Each slash/mark on the number line is 1/5, meaning that 6 marks away is 3 2/5.
To further explain how I know each mark is 1/5, each question had a denominator of 5, and if you count each mark from 2 1/5 (2 2/5, 2 3/5, 2 4/5, 3, etc) you will eventually land on 4 evenly.
A square metal sheet has the side length of 1 cm. À circular hole of radius 2/5 cm is drilled in the middle of the sheet.
How far the hole is from the edge of the sheet?
Step-by-step explanation:
PLEASE ASAP NEEDED SO BADLY PLEASEE PLEASE
Answer:
[tex]6x^{2} -24x-10[/tex] with remainder -5
Answer:
[tex]6^2-24x-10-\frac{5}{x+4}[/tex]
In other words, [tex]6x^2-24x-10[/tex] is the answer and -5 is the remainder
Step-by-step explanation:
I used long division for this, and I uploaded an image for the steps. The final answer I got was [tex]6x^2-24x-10-\frac{5}{x+4}[/tex]
Which of the following is a perfect square trinomial?
a. x^2+10x+25
b. x^2+6x+13
c. x^2+100
d. x^2+3x+9
Answer:
a. x² + 10x + 25
Step-by-step explanation:
because
(x + 5)² = (x + 5)(x + 5) = x² + 5x + 5x + 25 = x² + 10x + 25
so, it is a perfect square of (x + 5).
A line passes through the points ( p , a ) and ( p , − a ) where p and a are real numbers. If p = 0 , what is the y-intercept? Explain your reasoning.
The y-intercept of the linear function is y = 0.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The y-intercept is given by (0,a) = (0,-a). From this, we have that for it to be a function, a = -a, and the only value that respects this condition is a = 0, hence the y-intercept of the linear function is y = 0.
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Question 5 of 10
Identify an equation in slope-intercept form for the line parallel to y = 5x + 2
that passes through (-6, -1).
A. y = 5x + 29
B. y = -5x - 11
C. y = x +
OD. y = 5x - 29
SUMIT
Answer:
A
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is 5.
[tex]y+1=5(x+6) \\ \\ y+1=5x+30 \\ \\ y=5x+29[/tex]
The difference between two integers is 8 and their product is 65. Assume that the larger of the two numbers is x. Write a quadratic equation in standard form that can be used to determine the value of x. Factor your equation from Part B and determine the possible solutions to your equation. Show your work. Write an expression for the second number.
A quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0.
The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5.
The value for the second number is 5
Word Problem Leading To Quadratic Equation.The general formula for quadratic equation in a in standard form is
a[tex]x^{2}[/tex] + bx + c = 0
Given that the difference between two integers is 8
Let the two integers = x and y,
and their product is 65. If the larger of the two numbers is x. Then,
x - y = 8 and xy = 65
Since we are looking for the value of x, make y the subject of formula in the first equation.
y = x - 8
Substitute y in the second equation.
x(x - 8) = 65
[tex]x^{2}[/tex] - 8x - 65 = 0
[tex]x^{2}[/tex] - 13x + 5x - 65 = 0
(x - 13)(x + 5) = 0
x = 13 or -5
We will ignore -5 since x is the larger number.
To get y Substitute x in the second equation.
xy = 65
13y = 65
y = 65/13
y = 5
Therefore, a quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0. The Factor of the equation from Part B is (x - 13)(x + 5) and the possible solutions to the equation is x = 13 or -5. The value for the second number is 5
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Which statement is true regarding the graphed functions?
I need help and can’t find the answers anywhere
Answer:
f(0)=g(0)
Step-by-step explanation:
The problem is asking for where the output (y value) of one function, f(x), matches the output of another function, g(x), otherwise called an intersection. You can see that the two lines intersect at 0 on the x axis in the graph, therefore f(0)=g(0) meaning the outputs of f(x) are the same as g(x) at x value 0.
Find the perimeter of the rhombus below, given that a = 7 and b = 14. (round your answer to one decimal place, if necessary.)
If the value of a is 7, b is 14 in the rhombus then the perimeter of the rhombus is equal to 31.3 units.
Given that the value of a is 7,b is 14.
We are required to find the perimeter of the rhombus.
The values which are given to us are of the lengths of diagonals of rhombus.
Perimeter of the rhombus is equal to 4 times the side of the rhombus. So in order to find the perimeter of the rhombus we need the side of the rhombus not the diagonals.
When we draw the diagonals in the rhombus it forms four right angled triangle in which the Base is equal to 7/2 units and 7 is the perpendicular.
We have to use pythagoras theorem to find the hypotenuse which is the side of the rhombus.
Suppose base is BC , perpendicular is AB and hypotenuse is AC.
AC=[tex]\sqrt{7^{2} +7/2^{2} }[/tex]
=[tex]\sqrt{49+49/4}[/tex]
=[tex]\sqrt{245/4}[/tex]
=7.826
Perimeter of rhombus=4*side
=4*7.826
=31.304
After rounding off it will be 31.3 units.
Hence if the value of a is 7, b is 14 in the rhombus then the perimeter of the rhombus is equal to 31.3 units.
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If c(x) = 4x − 2 and d(x) = x² + 5x, what is (c.d)(x)?
4x³ + 18x² – 10x
x² + 9x-2
16x² + 4x-6
4x² + 20x-2
Answer:
[tex]4x^2+20x-2[/tex]
Step-by-step explanation:
To find (c.g)(x) we basically use the function d(x) as your variable, x, and plug it into c(x). So we replace every x in c(x) with the function d(x), [tex]x^{2} +5x[/tex]
c(g(x))=4(x^{2} +5x)-2
c(g(x))4[tex]x^2[/tex]+20x-2
Kindly solve this please!
Diagram for both the questions are given.
Answer:
Q9 - B) 8Q10 - D) 4.5========================
Question 9We have a diagram and need to find the number of routes without repeat paths:
[tex]ABCA[/tex] or [tex]ACBA[/tex]We can see that there is one route from A to B, two routes from B to C and two routes from C to A. This is same on reverse order.
This gives us the number of routes:
[tex]ABCA = 1*2*2 = 4[/tex][tex]ACBA = 2*2*1 = 4[/tex]Total number is:
[tex]4 + 4 = 8[/tex]The matching answer choice is B
---------------------------------------------------------------------------
Question 10From the given we can observe that:
ABC and DCE are similar triangles, since they have same angle at vertex E (vertical angles are equal) and both are right triangles.
From similarity we get same ratio of corresponding sides:
[tex]AE/DE = AB/CD = 3/9 = 1/3[/tex]We can find areas of triangles ACD and ECD and subtract to get the area of triangle AEC:
[tex]S_{ACD} - S_{ECD} = S_{AEC}[/tex]As per ratio of corresponding sides:
[tex]AE/DE = 1/3[/tex]As per segment addition:
[tex]AE + DE = AD = 4[/tex]From the two equations above we get:
[tex]DE = 3/4*AD = 3/4*4 = 3[/tex]Now, the required area is:
[tex]S_{ACD} - S_{ECD} = 1/2(4*9) - 1/2(3*9) = 4.5[/tex]This is matching the answer choice D
Answer:
9) B. 8
10) D. 4.5
Step-by-step explanation:
Question 9
For ease of visualization, label the different legs of the journey on the diagram (see attachment).
The journey needs to start and end at point A, go through points B and C (in any order), and not travel any road twice.
The different routes are:
AB (u), BC (x), CA (w)AB (u), BC (y), CA (w)AB (u), BC (x), CA (z)AB (u), BC (y), CA (z)AC (w), CB (x), BA (u)AC (z), CB (x), BA (u)AC (w), CB (y), BA (u)AC (z), CB (y), BA (u)Therefore, there are 8 different routes.
Question 10
Triangles EDC and EAB are similar since they have congruent angles:
∠EDC ≅ ∠EAB (both right angles)∠DEC ≅ ∠AEB (vertical angle theorem)Therefore, their corresponding sides are in proportion.
⇒ CD : BA = ED : EA
⇒ 9 : 3 = ED : EA
⇒ 3 : 1 = ED : EA
Since we know that AD = 4:
⇒ ED = 3
⇒ EA = 1
Area of a triangle
[tex]\sf Area = \dfrac{1}{2} \times base \times height[/tex]
To find the area of triangle AEC, subtract the area of triangle EDC from the area of triangle ADC.
[tex]\begin{aligned}\textsf{Area of triangle AEC} & = \sf Area\:of\:\triangle ADC - Area\:of\:\triangle EDC\\& = \sf \dfrac{1}{2} \cdot CD \cdot AD-\dfrac{1}{2} \cdot CD \cdot ED\\& = \sf \dfrac{1}{2}(9)(4)-\dfrac{1}{2}(9)(3)\\& = \sf 18-13.4\\& = \sf 4.5\:\:units\:squared\end{aligned}[/tex]
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Select the correct answer. which expression is equivalent to , if x > 0? a. b. c. d.
The equivalent expression of the expression is 128x^5y^6/2x^7y^5
How to determine the equivalent expression?The expression is given as:
128x^5y^6/2x^7y^5
Divide 128 by 2
64x^5y^6/x^7y^5
Apply the law of indices
64y^(6-5)/x^(7-5)
Evaluate the differences
64y/x^2
Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5
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Complete question
Select the correct answer. which expression is equivalent to 128x^5y^6/2x^7y^5 , if x > 0 and y > 0
In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor. Is there a significant difference between the proportions of urban and suburban residents who favor constructing nuclear plants
The p value for the difference is 0.005.
According to the statement
we have given that the 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor.
And we have to find the difference between them in proportions.
So,
X1 = 74 represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant
X2 = 70 represent the number of people suburban residents are in favor
N1 = 100 sample 1 selected
N2 = 125 sample 2 selected
AND
P1 = 0.74 represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant
And P2 = 0.56 represent the proportion of suburban residents are in favor And z would represent the statistic (variable of interest)
Pv represent the value for the test (variable of interest)
Here we apply the Z test to find the difference then
Z = (0.74 - 0.56) / (0.64(1-0.64)(1/100+1/125) )^1/2
Now after solving
Z = 2.795.
Now The significance level provided is ,and we can calculate the p value for this test.
Since is a two tailed test the p value would be:
P = (z>2,795)
P = 0.005.
So, The p value for the difference is 0.005.
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Please if anyone no math I really need help
Answer:
c
Step-by-step explanation:
option a (x-4) translates the graph 4 units right, not down
option b (x)-4 translates the graph 4 units down, not left
option c (x)+4 translates the graph 4 units up, so it is correct
option d (x+4) translates the graph 4 units left, not right
if the number is outside of the parentheses, like (x)+4 or (x)-4, the graph undergoes a vertical translation, and it moves up/down, with + meaning up and - meaning down
if the number is inside of the parentheses, like (x+4) or (x-4), the graph undergoes a horizontal translation, and moves left/right, with - meaning right and + meaning left
HELP PLS PLS!!!! look at pic
Answer: [tex]\frac{2}{25} +\frac{11}{25}i[/tex]
Step-by-step explanation:
To get the following you have multiply the conjugate. [tex]\frac{(2-i)(3-4i)}{(3+4i)(3-4i)}[/tex]
60% of UCLA is girls. What perrcentage are boys
.
Answer:
40%
Step-by-step explanation:
Percent must be equal to 100, so if 60 are girls, then 40% must be boys.
In the biblical account, adam lived to be how old?
a. 99
b. 122
c. 545
d. 930
A manufacturer makes ball bearings out of motel steel. it takes 5.24 cubic centimeters of molten steel to make ball bearings that each have a diameter of 1 centimeter
Using volume of ball bearings, a manufacturer makes 10 ball bearings from 5.2 cm³ of molten steel to make ball bearings that each have a diameter of 1 centimeter.
According to the question,
It takes 5.24 cubic centimeters of molten steel to make ball bearings that each have a diameter of 1 centimeter.
Radius = 1/2 = 0.5 cm
volume V of one ball bearing is: V=(4/3)*π*r³
= 4/3 * π * (0.5)³
=0.524 cm³
In order to find number of ball bearings out of molten steel only if we divide the volume of steel by the volume of the ball bearing
5.24/0.524=10.
Hence, using volume of ball bearings, a manufacturer makes 10 ball bearings from 5.2 cm³ of molten steel to make ball bearings that each have a diameter of 1 centimeter.
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Please help!
Which of these r-values represents the weakest correlation?
A. 0.2
B. 0.3
C. 0.4
D. 0.1
Answer: 0.1
Step-by-step explanation:
The smaller the absolute value of the correlation coefficient, the weaker the correlation.
Please help me
The sum of an integer and its square is 210. Find the integer. Include a completer
solution
Answer:
14
Step-by-step explanation:
An integers are whole numbers and their opposites. ...-3,-2,-2,0,1,2,3...
I just played with the numbers and found that 14 + 14^2 (14 squared is 14 x 14).
14 + (14)(14) = 210
Answer:
refer to the attachment
Adding and Subtracting Functions
F(x)=x^2+4
G(x)=x-1
Find (g+f)(x)
Answer:
Step-by-step explanation:
[tex](g+f)(x)=g(x)+f(x)=x-1+x^2 +4=x^2 +x+3[/tex][tex]x^2 +x+3[/tex]
Cora is wrapping a ribbon around a cylinder-shaped gift box. The box has a diameter of 15 inches and the ribbon is 60 inches long. Cora is able to wrap the ribbon all the way around the box once, and then continue so that the second end of the ribbon passes the first end. What is the central angle formed between the ends of the ribbon? Round your answer to the nearest tenth of a degree.
The central angle formed between the ends of the ribbon is 98.6°.
How to illustrate the angle?The circumference will be:
= πd
= 3.14 × 15 = 47.1
Ribbon = 60 - 47.1 = 12.9
Length of arc = x/360 × πd
12.9 = x/360 × 3.14 × 15
x = 98.6°
The angle is 98.6°
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Find the volume of a rectangular prism with the following dimension 2cm by 3cm by 4cm
Answer:
24 cm³
Step-by-step explanation:
V = LWH = 2 × 3 × 4 cm³ = 24 cm³
During a very cold winter, water pipes sometimes burst because:
The water pipe sometimes bursts in winter because of the flowing water getting transformed into freezing water due to drop in temperature and the volume increases creating more pressure on the wall pipes.
Bursting of Water Pipes During a Very Cold Winter
The straightforward explanation is that during very cold winters, as water freezes into ice, it expands, causing solid ice to fill a larger volume than the liquid that was previously flowing through the pipes.
As we know that, the pressure P increases with increase in volume, V, the increased volume of frozen water leads to increase in the pressure inside the pipe.
The pressure that the ice builds up inside the pipes could rupture the pipe walls.
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Which term describes the red curve in the figure below?
• A. Hyperbola
B. Circle
C. Parabola
• D. Ellipse
A cone has a circular base. So, the answer to your question is B for circle.
A DVD player costs $96.34, with sales tax included. What is the original price of the DVD player if the sales tax rate is 8.25%?
The original price of the DVD player if the sales tax rate is 8.25% is $88.79
Sales taxCost of DVD player including tax = $96.34Sales tax = 8.25%Original cost = 8.25%Total cost = original cost + (sales tax × original cost
96.34 = x + (8.5% × x)
96.34 = x + (0.085 × x)
96.34 = x + 0.085x
96.34 = 1.085x
x = 96.34 / 1.085
x = 88.7926267281105
Approximately,
x = $88.79
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Chemotherapy in adult highgrade glioma: a systematic review and metaanalysis of individual patient data from 12 randomized trials
Systemic chemotherapy's impact on survival and recurrence in people with high-grade glioma has not been conclusively studied.
What is Systemic chemotherapy?Patients undergoing systemic chemotherapy can get their chemotherapy drugs intravenously or orally. The medication may be injected into the body intravenously, or through an IV, or intramuscular, into a muscle (IM).
Some Key features of systemic chemotherapy are-
Background: In order to evaluate the effects of such treatment on survival and recurrence, we conducted a systematic review and meta-analysis.Methods: From 12 randomised controlled studies, information on 3004 patients was incorporated (11 published and one unpublished).Findings: Overall, the findings indicated a significant survival extension associated with chemotherapy, with a hazard ratio of 0.85 (95 percent confidence interval [CI] 0.78–0.91, p0.0001) or a relative reduction in mortality risk of 15%. There was no proof that a patient's age, gender, histology, performance status, or degree of resection affected how chemotherapy worked in any particular way.Interpretation: Further research into pharmacological treatment for malignant tumors is encouraged by this modest but noticeable improvement in survival from chemotherapy.To know more about Chemotherapy, here
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6. At the local community center, they've decided to build a pool in the
shape of a rectangular prism. The length of the pool is 27 feet and the
depth is 12 feet. Also, the area of the base of the pool must be 864 square
feet. What is the width of the pool?
32 feet
64 feet
13.7 feet
123 feet
Answer:
width = 32 ft
Step-by-step explanation:
Divide the base area (864 ft^2) by the length (27 ft). We don't need to know the depth of the pool to solve this problem.
864 ft^2
------------- = width = 32 ft
27 ft
Which side lengths form a right triangle?
Choose all answers that apply:
A:
11,13,√290
B:
7, 24, 25
C: 2, 5, 7
The side lengths that forms a right triangle are as follows:
11, 13 √2907, 24, 25What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides of the triangle follows Pythagoras theorem.
Therefore,
c² = a² + b²
where
a and b are the legsc is the hypotenuseThe hypotenuse is the longest side of the right triangle.
Therefore, the side lengths that forms a right triangle are as follows:
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Jeri finds a pile of money with at least $\$200$. If she puts $\$80$ of the pile in her left pocket, gives away $\frac{1}{3}$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $\$200$ of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)
Solving an inequality, we will see that there is less than $280 in the pile of money.
How much money is originally in the pile?Let's say that the amount of money is defined by the variable.
First, we know that Jeri keeps $80, so now in the pile we have:
M - $80.
Now she gives one third of that, then the leftover is:
(2/3)*(M - $80) + $80
We know that this is more than:
M - $200
Then we have the inequality:
(2/3)*(M - $80) + $80 > M - $200
And we can solve this for M.
(2/3)*M - (2/3)*$80 + $80 > M - $200
(1/3)*$80 + $200 > M - (2/3)*M
(1/3)*$80 + (1/3)*$200 > (1/3)*M
$280 > M
Then we conclude that there is less than $280 in the pile of money.
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