Answer:
[tex]x=\frac{17+\sqrt[]{241}}{8},\frac{17-\sqrt[]{241}}{8}[/tex]Explanation:
Given the below function;
[tex]f(x)=4x^2-17x+3[/tex]Note that a quadratic equation in standard form is generally given as;
[tex]y=ax^2+bx+c[/tex]If we compare both of the equations above, we can deduce that;
[tex]a=4,b=-17,c=3[/tex]We'll now use the below quadratic formula to solve for the values of x as seen below;
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{17\pm\sqrt[]{(-17)^2-4\cdot4\cdot3}}{2\cdot4} \\ x=\frac{17\pm\sqrt[]{289-48}}{8} \\ x=\frac{17\pm\sqrt[]{241}}{8} \\ \therefore x=\frac{17+\sqrt[]{241}}{8},\frac{17-\sqrt[]{241}}{8} \end{gathered}[/tex]
Us the bar graph to find the experimental probability of rolling at least 3.
The total number of times the cube was rolled is 13 + 16 + 15 + 17 + 19 + 20 = 100
The experimental probability for each number rolled is given by:
P(1) = 13/100 = 13%
P(2) = 16/100 = 16%
P(3) = 15/100 = 15%
P(4) = 17/100 = 17%
P(5) = 19/100 = 19%
P(6) = 20/100 = 20%
Therefore, the probability of rolling at least 3 is given by:
P(>=3) = P(3) + P(4) + P(5) + P(6) = 15% + 17% + 19% + 20% = 71%
Antonio mechanic charged $75 for a radiator and $50 per hour for labor. the total cost to install the radiator was $325 Approximately how long did it take the mechanic to install 5th e radiator
Given data:
The given fixed cost is $75.
The labor charges per hour is $50.
The expression for the total call is,
[tex]\begin{gathered} 325=75+(50)x \\ x=5 \end{gathered}[/tex]Thus, the value of time is 5 hours, so option (B) is correct.
Please help
question is attached below
what is the expression in rational exponent form?
8^1/4 is the simplified form of the expression ( ⁴√8³ )^1/3 in rational exponent form.
What is the simplified form of the expression?Power of a power rule simply states that "if a base raised to a power is being raised to another power, the base remains the same while the exponents are multiplied
Given the expression in the question;
( ⁴√8³ )^1/3
To simplify, we apply the law of exponents
ⁿ√aˣ = a^(x/n)
( ⁴√8³ )^1/3
( 8^3/4 )^1/3
Now, using power rule. multiply the exponents.
( zᵃ )ᵇ = zᵃ ˣ ᵇ
( 8 )^3/4 × 1/3
( 8 )^( 3×1 / 4×3 )
( 8 )^( 3 / 12 )
( 8 )^( 1/4 )
8^1/4
Therefore, the simplified form of the expression is 8^1/4.
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7-5x-10+3x simplified the expression
Simplify the expression 7-5x-10+3x.
[tex]\begin{gathered} 7-5x-10+3x=-5x+3x-10+7 \\ =-2x-3 \end{gathered}[/tex]So answer is -2x-3.
While waiting for the school bus, Rachelle records the colors of all cars passing through an intersection. The table shows the results. Estimate the probabithe next car through the intersection will be silver. Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Answer:
26.1%
Explanation:
Taking into account the table, we can calculate the total number of cars as follows
12 + 9 + 20 + 5 = 46
Then, from thos 46 cars, 12 are silver. So, the probability that the next car will be silver is equal to:
P = 12/46 = 0.261
Which written as a percentage is equal to
0.261 x 100 = 26.1%
Therefore, the answer is 26.1%
Find the area of the sector, given central angle of 70 degrees and a radius of 6. Leave your answer in terms of π.
The rule of the area of a sector which has radius r and central angle x degrees is
[tex]A=\frac{x}{360}\times\pi r^2[/tex]Since the central angle is 70 degrees, then
[tex]x=70^{\circ}[/tex]Since the radius of the circle is 6, then
[tex]r=6[/tex]Substitute them in the rule above
[tex]\begin{gathered} A=\frac{70}{360}\times\pi\times6^2 \\ \\ A=\frac{70}{360}\times\pi\times36 \\ \\ A=7\pi \end{gathered}[/tex]The answer is
The area of the sector is 7pi square units
Toussaint l ouverture led a revolt in the 1790s that freed Haiti
the grocery store sells ice cream in 108 fl. oz. containers. How many pints of ice cream is there in 3 of the ice cream containers?
The container they sell ice cream = 108 fluid oz
The amount of fluid oz the 3 ice cream container contains will be as follows
[tex]\begin{gathered} \text{amount of 3 ice cream container=3}\times108=\text{ }324\text{ fluid oz} \\ \end{gathered}[/tex]Amount of pints will be as follows
[tex]\begin{gathered} \text{6 fluid ounces}=1\text{ cup} \\ 324\text{ fluid ounces=?} \\ \text{cross multiply} \\ \text{amount in cups=}\frac{324}{6}=54\text{ cups} \\ \\ 2\text{ cups= 1pint} \\ 54\text{ cups=?} \\ \text{cross multiply} \\ \text{amount of 3 of the ice cream container in pints=}\frac{54}{2}=27\text{ pints} \end{gathered}[/tex]Which of the following describes GE check all that applyDF=18
Since DF=18; then,
[tex]\begin{gathered} DF=18 \\ \text{and} \\ DF=FG+GD \\ \Rightarrow FG+GD=18 \\ \Rightarrow3a+a+6=18 \\ \Rightarrow4a=12 \\ \Rightarrow a=3 \\ \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \Rightarrow FG=9,GD=9 \\ \Rightarrow\Delta\text{EFG}\cong\Delta EDG \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow\angle FEG\cong\angle\text{DEG} \\ \Rightarrow EG\text{ is angle bisector of }\angle E \end{gathered}[/tex]Furthermore, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. As we proved above, G is the midpoint of segment FD; thus, GE is a median of triangle DEF.
However, we do not have any information regarding the angles besides
Hence, the answers are Angle bisector and Median.
Washington State Credit Union pays 9.5% interest, compounded daily, from the date of deposit to the date of withdrawal. The daily interest rate (to the nearestmillionths place) for May 23 (91 days in the quarter) on this account is:0.0002540.0002610.0002700.000249None of these choices are correct.
Interest, r, is 9.5%,
Number of days, n, is 91 days,
Let P represent the principal
t is number of times
Where i = (r/365) for daily compounded interest,
[tex]Daily\text{ compounded interest = }P(1+i)^n-P[/tex][tex]\begin{gathered} \text{Daily compounded interest = P(1+}\frac{9.5}{365})^{91}-P \\ =P(1+0.02603)^{91}-P \\ =P(1.02603)-P \\ =1.02603P-P \\ =0.02603 \end{gathered}[/tex]Hence, the best option is B.
||| Classifying scalene, isosceles, and equilateral triangles by side... For each triangle, check all that apply. Triangle A 10' Scalene Isosceles O Equilateral Triangle B 40° 40° 100° O Scalene O Isosceles O Equilateral Triangle C 60° 60° O Scalene Isosceles. Equilateral 60° Triangle D 5 11 Scalene Isosceles Equilateral W X
ANSWER:
EXPLANATION:
Given:
To:
Check all that apply
A scalene triangle is a triangle in which all three sides have different lengths and all three angles have different measures.
An isosceles triangle is a triangle that has two sides of equal length and angles opposite to the two equal sides are congruent.
An equilateral triangle is a triangle in which all three sides have equal lengths. It is also equiangular, that is, all angles are congruent.
From the above definitions, we can go ahead and check all that apply as seen below;
Use the graph of y = ef to evaluate the expression e-1.5. Round the solution to the nearest tenth if necessary.
The solution lie in tracing -1.5 on the x axis to the graph.
In this case, it is 0.2.
The graphs below have the same shape. f(x) = x^2.What is the equation of the graph of g(x)?O A. g(x) = x^2 + 4O B. g(x) = x^2 - 4O C. g(x) = (x+ 4)^2O D. g(x)= (x-4)^2
ANSWER :
D. g(x) = (x - 4)^2
EXPLANATION :
Note that the translation in parabola :
[tex]\begin{gathered} f(x)=(x\pm c)^2 \\ \text{ where c is the horizontal movement} \\ \text{ c is positive if the movement is to the left} \\ \text{ c is negative if the movement is to the right} \end{gathered}[/tex]From the graph, g(x) is 4 units to the right of f(x)
Then c must be -4
[tex]g(x)=(x-4)^2[/tex]De Andrea is studying metals. She finds out that the ratio of chromium to nickel instainless steel is 9 to 4. If De'Andrea has 27 pounds of chromium, how many pounds ofnickel will she need to forge stainless steel? Show your work.
Ratio:
chromium / nickel = 9/4
27 pounds of chromium
x pounds of nickel
Replacing:
27/x = 9/ 4
Solve for x
Cross -multiply:
27 (4) = 9x
108 = 9x
Divide both sides by 9
108/9 = 9x/9
12 = x
Answer:
She will need 12 pounds of nickel
Peter drives 720km from Johannesburg to Phalaborwa in 7 hours 30 minutes. Manaka drives 1560km from Fish Hoek to Pretoria in 15 hours. which driver maintained a higher average speed
Average speed of Peter:
720 km / 7.5 hours (Since 30 minutes is equal to 0.5 hours)
96 km/h (Simplifying)
Average speed of Manaka:
1560 km / 15 hours
104 km/h (Simplifying)
Manaka maintained a higher average speed.
I need help with this, struggling to solveIt’s from my ACT prep guide
Given the expression:
[tex]\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\sec (-\pi)[/tex]We will find each trigonometric function the substitute into the expression
We will find each value with the help of the reference angle
[tex]\tan (-\frac{2\pi}{3})=\tan (\frac{4\pi}{3})=\tan (\pi+\frac{\pi}{3})=\tan (\frac{\pi}{3})=\sqrt[]{3}[/tex][tex]\sin (\frac{7\pi}{4})=\sin (2\pi-\frac{\pi}{4})=-\sin (\frac{\pi}{4})=-\frac{1}{\sqrt[]{2}}[/tex][tex]\sec (-\pi)=\sec (-\pi+2\pi)=\sec \pi=-1[/tex]Substitute with the recent values:
[tex]\begin{gathered} \frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\sec (-\pi)=(\sqrt[]{3}\div-\frac{1}{\sqrt[]{2}})-(-1) \\ \\ =(\sqrt[]{3}\cdot(-\sqrt[]{2}))+1=-\sqrt[]{6}+1 \end{gathered}[/tex]So, the answer will be:
[tex]-\sqrt[]{6}+1[/tex]The following table represents a relation.x y−3 00 −25 −311 −2Does the table represent y as a function of x?Why or why not?
Given the table:
x y
-3 0
0 -2
5 -3
11 -2
Let's determine if the table represents y as a function of x.
When we say y as a function of x, it means the y value depends on x values.
For a relation to be a function, there must be one value of y for every unique value of x. This means one value of x must not appear twice.
From the given table, no value of x is repeated. Hence, we can say there is one value of y for every value of x.
Therefore, the table represents a function because there are no x-values with more than one y-value.
ANSWER:
Yes, because there are no x-values with more than one y-value.
13. The owner of an apple orchard recorded the number of pounds of apples produced by each
below show the results.
tree of a certain type and the age of each tree of that type. The scatter plot and line of best fit
Apples Produced
114.300
Pounds of Apples
400
350
300
250
200
150
100
50
19. 150)
0
2 4 6 8 10 12 14 16
Age of Tree (years)
Select the two statements that correctly interpret key features of the line of best fit.
A The x-intercept of the line of best fit indicates that a tree will not produce any apples in
the first 4 years.
B. The slope of the line of best fit indicates that a tree will produce an additional 30 pounds
of apples each year once the tree begins producing apples.
c. The y-intercept of the line of best fit indicates that a tree will produce 300 pounds of
apples in the first year.
D The slope of the line of best fit indicates that the rate of increase in apple production of a
tree is 6 pounds per year
E The y-intercept of the line of best fit indicates that a tree will produce 4 pounds of apples
each year
Let's find the slope of best fit:
[tex]\begin{gathered} (x1,y1)=(9,150) \\ (x2,y2)=(14,300) \\ m=\frac{y2-y1}{x2-x1}=\frac{300-150}{14-9}=\frac{150}{5}=30 \end{gathered}[/tex]So, we can conclude that statement B is correct.
Also from the graph we can conclude that the line starts from x = 4 approximately, therefore the statement A is also correct.
li's total monthly expenses consist of room and borad: $610 car payment : $278 ; gas : $151 ; insurance: $112; and miscellaneous expenses: $223. estimate lies monthly expenses. (type a whole number)
Li's total monthly expenses are:
610+275+151+112+223=885+263+223=1371 dollarsThree tables are placed side by side. One table is 4 feet 9 inches wide, another is 5 feet 11 inches wide, and the third is 2 feet 10 inches wide. How wide arethey combined?Write your answer in feet and inches. Usenumber less than 12 for inches.
We have 3 tables that are placed side by side.
We have to find the final width of them combined.
Then, the final width will be the sum of the width of the 3 tables:
[tex]\begin{gathered} W=w_1+w_2+w_3 \\ W=9in+11in+10in \\ W=30in \end{gathered}[/tex]We know that the total width is 30 in, but we need to express it as feet and inches.
Knowing that 1 foot is 12 inches, we wan divide the total width by 12 and see how many feet it represents:
[tex]W=\frac{30in}{\frac{12in}{1ft}}=2.5ft[/tex]So we will express this width as 2 ft plus a remaining quantity in inches. This remaining quantity is 0.5 ft, but we have to convert it to inches.
To do that, we use the equivalency 12 inches = 1 foot, and multiply the remaining quantity to express it in inches:
[tex]0.5ft\cdot\frac{12in}{1ft}=6in[/tex]Then, we add the 2 feet and the final width results in 2 feet and 6 inches.
Ans
Represent the following sentence as an algebraic expression, where’s “a number” is the letter xA number is divided by 1
The expression "a number is divided by 1" can be written algebraically like this:
[tex]\frac{x}{1}[/tex]Suppose that y varies inversely with x, and y=3 when x=4.
When y varies inversely as x it can be expressed as follows:
[tex]\frac{1}{x}\text{ }\propto\text{y}[/tex]If we write the general equation for this
[tex]y=\frac{A}{x}[/tex]When y=3 and x=4 we can calculate de value of A
[tex]\begin{gathered} x=4 \\ y=3 \\ 3=\frac{A}{4} \\ A=4\cdot3 \\ A=12 \end{gathered}[/tex]Then the equation that describes an inverse variation between x and y is_
[tex]y=\frac{12}{x}[/tex]Patrick had 93 cameras and he purchased 86 more, Patrick wants toship all of his cameras across the country using boxes that hold 65cameras each. How many full boxes can he ship?
Given that Patrick had 93 cameras and purchased 86 more, the total number of cameras he has is
= 93 + 86
= 179 cameras
Given that one box can only hold 65 cameras, the total number of boxes required can be derived as
= 179/65
= 2 49/65
Hence he would require 3 boxes. The first will hold 65, the next will hold another 65 and the third will hold the remaining 49 cameras. Thus he can ship 2 full boxes while the 3rd will only hold 49 camera
o is between b and t
We can draw the line to help us
The whole segment is 14, and the segment TO is 3. Therefore the segment BO will be BT minus OT, then
[tex]\begin{gathered} BT=BO+OT \\ BO=BT-OT \\ BO=14-3 \\ BO=11 \end{gathered}[/tex]Hence the length of BO is 11
What are the values of the two 3s in 3,435
We have the next number
[tex]3,435[/tex]the value of the first 3 counting right to the left
is 30
because is placed in the tens
the value of the second 3 counting right to the left
is 3000
because is placed in the thousands
The range of f(x)=|x| is y≥0. If a<0 for g(x)=a|x|, what is the range of function g?
We have the following:
[tex]\begin{gathered} f\mleft(x\mright)=|x| \\ R=y\ge0 \\ \text{ now,} \\ a<0 \\ g(x)=a|x| \end{gathered}[/tex]Being a less than 0, all the values that are multiplied were less than zero or zero, because even if a does not include 0, x can be 0, therefore, the range would be:
[tex]y\leq0[/tex]The answer is the option D
Consider Circle E. Segment CD is the perpendicular bisector of AB.What is the measure of the arc intercepted by
Consider the Circle E. Segment CD is the perpendicular bisector of AB.
What is the measure of the arc intercepted by
The measures of the arc = 2 π *r* ∠ / 360º
Segment CD is the perpendicular bisector of AB, the angles = 90º
The measures of the arc = 2 π * r* 90º / 360º
The measures of the arc = 2 π * r* (1 / 4)
__________________________________________
The measures of the arc = π *r/ 2
The measure of the arc intercepted by AC is {2πAE}(1/4)rad.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know the arc length of a circle is 2πr(Ф/360).
Where r is the radius, Ф is the angle the arc is making it the center.
Given, Circle E. Segment CD is the perpendicular bisector of AB.
∴ m∠CAE = 90°.
And AE = CE = BE = DE = r.
∴ [tex]ARC_{AC}[/tex] = 2π(AE)(90/360).
[tex]ARC_{AC}[/tex] = 2πAE(1/4).
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On a coordinate plane, the horizontal axis is called the _______-axis and the vertical axis is called the _______-axis.Question 1 options:y, xx-y, y-xy-x, x-yx, y
ANSWER
D. x, y
On a coordinate plane, the horizontal axis is called the x-axis, and the vertical axis is called the y-axis.
EXPLANATION
In coordinate planes, the x-coordinate is given by the horizontal axis, so it is called the x-axis, while the y-coordinate is given by the vertical axis, so this is called the y-axis.
Jacob earns $7 for every lawn he mows. Help him find his total earnings in d, dollars. Use the equation 7L = D to fill in the table. Then plot the points on the graph. Connect the points to make a line.
ANSWER and EXPLANATION
The equation that represents the situation is:
[tex]\begin{gathered} D=7L \\ \text{where D = amount he earns} \\ L=\text{ number of lawns mowed} \end{gathered}[/tex]To fill the table, substitute the value of L and find the corresponding value of D and vice versa:
[tex]\begin{gathered} \text{when L = 1:} \\ D=7\cdot1 \\ D=\text{ \$7} \end{gathered}[/tex][tex]\begin{gathered} \text{when D = 21:} \\ 21=7\cdot L \\ L=\frac{21}{7} \\ L=3\text{ lawns} \end{gathered}[/tex][tex]\begin{gathered} \text{when L = 4:} \\ D=7\cdot4 \\ D=\text{ \$28} \end{gathered}[/tex]Now, plot the graph:
Which graph represents the piecewise-defined function? Y={6 if x ≤-3. 3 if-32
A piecewise function is a function that is defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain (a sub-domain)
The three sub-functions are ;
y = 6
y = 3
y = 5
These three functions exist at a certain domain on the x-axis as shown.
From the graphs shown, the one that represents the piecewise function given is the first graph on the left.
It is shown below;