Answer:
A) f(0) = -7
B) f(-3) = 44
C) x = -1, (7/5)
Step-by-step explanation:
2. Let f(x) = 5x² - 2x - 7.
(a) find f(0)
f(x) = 5x² - 2x - 7
f(0) = 5(0)² - 2(0) - 7
f(0) = -7
(b) find f(-3)
f(x) = 5x² - 2x - 7
f(-3) = 5(-3)² - 2(-3) - 7
f(-3) = 5(9) - 2(-3) - 7
f(-3) = 45 + 6 - 7
f(-3) = 45 + 6 - 7
f(-3) = 44
(c) find x if f(x) = 0
f(x) = 5x² - 2x - 7
f(x) = 5x² - 2x - 7 = 0
(5x² + 5x)(-7x - 7)
5x(x + 1) -7(x + 1)
(5x - 7)(x + 1)
5x - 7 = 0, x + 1 = 0
+7 +7 -1 -1
--------------- ---------------
5x = 7 x = -1
÷5 ÷5
------------
x = (7/5)
5(-1)² - 2(-1) - 7 = 0
5(7/5)² - 2(7/5) - 7 = 0
----------------------------------------------------------------------------------------------------------
I hope this helps!
The rear windshield wiper blade on a car has a length of
10
inches. The blade is mounted on a
18
inch arm,
8
inches from the pivot point. If the wiper turns through an angle of
145
degrees, how much area is swept clean?
The area that is swept clean by the wiper is 329.13 inches².
What is the Area of the Sector?The area of a circle encompassed between its two radii and the arc next to them is known as the sector of a circle. A circle's sector area is the total area contained inside the sector's perimeter.The following formulas can be used to determine a sector's area: Area of a Sector of a Circle = (θ/360°)πr², where r is the circle's diameter and θ is the sector angle, in degrees, that the arc at the center subtends.Given:
Radius of arm(r₁) = 18 inch
Length of wiper blade = 10 inches
Radius of the point at which the blade is mounted(r₂) = 8 inches
Angle of the sector,θ = 145°
Required Area is calculated as,
Area = (θ/360°)πr₁² - (θ/360°)πr₂²
= (θ/360°) (πr₁² - πr₂²)
= (145°/ 360°) π(18² - 8²)
= (145°/ 360°) π(324 - 64)
= 329.13 inches²
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The airport parking lot charges $2.00 to enter and $3.00 per hour after that. Carmen has N dollars and wants to be able to determine the maximum number of hours she can park. How can Carmen determine the length of time she can afford to park her car in the parking lot? Justify your answer.
The equation of the time she can afford to park her car is 2 + 3t = N
How to determine the time she can afford to park her carThe given parameters are
Entrance charge = $2.00Rate per hour = $3.00Assume she stays for t number of hours, the total charges would be
Total = Entrance charge + Rate per hour * Number of hours
This gives
Total = Entrance charge + Rate per hour * t
Substitute the known values in the above equation
So, we have
Total = 2 + 3t
From the question, she has N dollars
So, we have
2 + 3t = N
Hence, the expression of the description is 2 + 3t = N
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АBсDIf AC = 22x - 19, find x. Round your answer to the nearest tenth ifnecessary.AB = 4x + 31BC = 29
Answer:
The value of x is equal to 4.4.
[tex]x=4.4[/tex]Explanation:
Given;
[tex]\begin{gathered} AC=22x-19 \\ AB=4x+31 \\ BC=29 \end{gathered}[/tex]The length AC is the sum of length AB and BC;
[tex]AC=AB+BC[/tex]substiuting the given values;
[tex]\begin{gathered} AC=AB+BC \\ 22x-19=4x+31+29 \\ 22x-19=4x+60 \end{gathered}[/tex]let's add 19 to both sides, and then subtract 4x from both sides;
[tex]\begin{gathered} 22x-19=4x+60 \\ 22x-19+19=4x+60+19 \\ 22x=4x+79 \\ 22x-4x=4x-4x+79 \\ 18x=79 \end{gathered}[/tex]divide both sides by 18;
[tex]\begin{gathered} \frac{18x}{18}=\frac{79}{18} \\ x=4.388888 \\ x=4.4 \end{gathered}[/tex]The value of x is equal to 4.4.
[tex]x=4.4[/tex]A crane has a cable with a breaking strain of 6400 kg
measured to 2 significant figures.
It is used to lift crates which weigh 90 kg measured to the nearest 10 kg.
What is the
greatest number of crates that can safely be lifted
at one time without breaking the cable?
Some working must be shown.
The greatest number of crates that can safely be lifted at one time without breaking the cable is 71.
What is GCF?
The biggest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x, and y. The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD). GCF is usually always utilised with fractions, which are frequently employed in daily life. You can obtain the necessary reduced form by determining the GCF of the denominator and numerator of a fraction or ratio.
A crane has a cable with a breaking strain of 6400 kg measured to 2 significant figures. It is used to lift crates which weigh 90 kg measured to the nearest 10 kg.
We need to calculate the greatest number of crates that can safely be lifted at one time without breaking the cable.
According to the question,
It is given that, the breaking strain of the crane is 6,400 kilograms and each crate is 90 kilograms.
Thus, to know the number of crates (n) that can safely lift is equal to the weight of the crane is 6,400 kilograms divided by is 90 kilograms.
thus,
[tex]n=\frac{weight of the crane}{weight of each crate}\\ \\n=\frac{6400}{90}[/tex]
so, n= 71.111≈71
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Rodney opens a savings account with $75 and also deposits $40 each month. Morgan opens an account with $50 and also deposits $40 each month. Will they have the same amount in their account at any point? If so, after how many months? Explain.
Show an equation
No, they will not have the same amount in their account at any point of time.
Given that:-
Money deposited by Rodney at the opening of savings account = $ 75
Money deposited by Rodney each month in the account = $ 40
Money deposited by Morgan at the opening of savings account = $ 50
Money deposited by Morgan each month in the account = $ 40
Let us imagine that they will have equal amount of money in their accounts at a particular point of time.
Let us consider x to be the number of months when they will have same amount of money in their account.
Hence, we can write,
75 + 40x = 50 + 40x
We can see that,
75 - 50 = 40x - 40x
25 = 0
But this is not possible.
Hence, they will never have the same amount of money in their accounts at a particular point of time.
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Find the probability of the following card hands from a 52-card deck. In poker,
aces are either high or low. A bridge hand is made up of 13 cards.
In poker, four of a kind (4 cards of the same value)
O 2.40 x 104
O 2.00 × 10-5
O 1.85 x 10-5
O4.34 x 10-4
Answer: 2.40 * 10^(-4)
This value is approximate.
=====================================================
Explanation:
A four of a kind is where we have 4 cards of the same value, as mentioned in the instructions. For example, we could have 4 queens and some other card, such as a 10 of clubs.
There are 13 cards to pick from for any given suit. Once that card is chosen, the other 3 slots are fixed to whatever that first card is. The fifth slot will have 52-4 = 48 choices.
In short we have 13 choices for the first four cards and 48 choices for the fifth card.
Overall we have 13*48 = 624 different four of kind poker hands.
Let's now calculate how many possible poker hands there can be.
A poker hand consists of 5 cards. I don't know why your teacher mentioned a bridge hand of 13 cards since that's for a different game.
We'll use n = 52 and r = 5 in the nCr combination formula below.
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\52 C 5 = \frac{52!}{5!*(52-5)!}\\\\52 C 5 = \frac{52!}{5!*47!}\\\\52 C 5 = \frac{52*51*50*49*48*47!}{5!*47!}\\\\ 52 C 5 = \frac{52*51*50*49*48}{5!}\\\\ 52 C 5 = \frac{52*51*50*49*48}{5*4*3*2*1}\\\\ 52 C 5 = \frac{311875200}{120}\\\\ 52 C 5 = 2598960\\\\[/tex]
There are 2,598,960 possible five-card poker hands.
624 of those hands are four of a kind, so the probability we want is
624/(2,598,960) = 0.000240 = 2.40 * 10^(-4)
The approximate decimal value 0.000240 converts to 0.0240%
equations that are parallel to y=2x+11
y = 2x is the equation that is parallel to the given line in the question .
WHAT IS PARALLEL LINE ?If two non-vertical lines in the same plane have the same slope, they are said to be parallel. Never will two parallel lines cross. If two non-vertical lines in the same plane cross at a right angle, they are said to be perpendicular.
CALCULATIONy = 2x + 11
choose a point which the line will pass through
(0,0)
using y = mx + b
m = 2
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
[tex]y_{2} - y_{1} = m(x_{2} - x_{1} )[/tex]
y - 0 = 2x -0
y = 2x
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The measure of DF the center of the given circle
Solution:
Given the circle;
[tex]|OF|\cong|OE|=r[/tex]Thus;
[tex]\triangle FOE\text{ is isosceles triangle}[/tex]Then;
[tex]\begin{gathered} \angle OFE=38^o \\ \\ \angle Arc\text{ }DF=38^o+38^o..............(\text{ An exterior angle of a triangle is equal to the sum of the two interior opposite angles\rparen} \\ \\ \angle Arc\text{ }DF=76^o \end{gathered}[/tex]CORRECT OPTION: B
Please answer question 8, I’d really appreciate it!!
Answer:
t = 8
Step-by-step explanation:
1. 2.5(t-2)-6 = 9 = 2.5t-5-6=9
2. add common terms = 2.5t - 11 = 9
3. add 11 on both sides to eliminate the 11
4. 2.5t= 20
5. 20/2.5 = 8
6. t = 8
Jennifer bought a bracelet at original cost $25 to sell in her handicraft store. She marked the price up 45%.
a) Find the amount of the mark-up price.
S
b) Find the list price.
S
(Round to two decimal places if necessary.)
(Round to two decimal places if necessary.)
Answer:
Mark up $11.25
Selling price $36.25
Step-by-step explanation:
25(.45) = 11.25 This is the mark up, The selling price is then 25 + 11.25, which is $36.25
A car uses 3 1/8 gallons of gasoline per hour when driving on the highway. How many gallons will it use after 4 2/3 hours? It will use _____________ gallons.
If the car uses 3 1/8 gallons per hour and the number of hours is 4 2/3, we can multiply both values to find the total amount of gallons used in this time.
First, we need to convert 3 1/8 and 4 2/3 into improper fractions:
[tex]\begin{gathered} 4\text{ }\frac{2}{3}=4+\frac{2}{3}=\frac{12}{3}+\frac{2}{3}=\frac{14}{3}\\ \\ 3\text{ }\frac{1}{8}=3+\frac{1}{8}=\frac{24}{8}+\frac{1}{8}=\frac{25}{8} \end{gathered}[/tex]Now, multiplying the values, we have:
[tex]\frac{25}{8}\cdot\frac{14}{3}=\frac{350}{24}=14.58[/tex]So the car will use 14.58 gallons.
Twice a number minus another numberis 8. Their sum is -2. Find thenumbers.
Set x and y to be the two numbers we need to find; then, according to the question,
[tex]\begin{gathered} 2x-y=8 \\ and \\ x+y=-2 \end{gathered}[/tex]Solve the system of equations as shown below
[tex]\begin{gathered} \Rightarrow y=2x-8 \\ \Rightarrow x+(2x-8)=-2 \\ \Rightarrow3x=6 \\ \Rightarrow x=2 \end{gathered}[/tex]Finding y,
[tex]\begin{gathered} x=2 \\ \Rightarrow y=2*2-8=-4 \\ \Rightarrow y=-4 \end{gathered}[/tex]Thus, the answer is 2 and -4, option E.Solve for .
5x - 4 ≥ 12 OR 12x + 5 < -4
Answer:[tex]x\geq 3.2[/tex] and [tex]x < -0.75[/tex]
Step-by-step explanation
[tex]5x-4\geq 12[/tex]
First you would add 4 to each side.
[tex]5x\geq 16[/tex]
Then divide each side by 5.
[tex]x\geq 3.2[/tex]
Next one,
[tex]12x+5 < -4[/tex]
First you would subtract 5 from both sides.
[tex]12x < -9[/tex]
Then divide both sides by 12.
[tex]x < -0.75[/tex]
Adult male heights have a normal probability distribution with a mean of 70 inches and a standard deviation of 4 inches.
What is the probability that a randomly selected male is more than 70 inches tall?
There is a 0.5 percent probability that a randomly chosen male will be taller than 70 inches.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.So,
Mean height of the adults: μ = 70 inchesThe standard deviation: σ = 4 inchesThen, the formula will be:
Z = x-μ/σInsert the values in the formula as follows:
Z = x-μ/σZ = 70-70/4Z = 0Then,
0.5 is the p-value at z=0.P(x>70)=1-P(x<70)=1-0.5 = 0.5Therefore, there is a 0.5 percent probability that a randomly chosen male will be taller than 70 inches.
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The size of the graduating class of Kyle’s school has been growing at a constantrate. Kyle’s older brother’s class had 257 students when he graduated in 2015. Kyleis going to graduate in 2018, and his class has 329 students. Write a linear function that models the school’s graduating class size (y) in terms of the year (x).
The linear equation that models the school’s graduating class size (y) in terms of the year (x) after 2015 is given as y = 24x + 257
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
Let y represent the graduating class size in terms of the year (x) after 2015.
Kyle’s older brother’s class had 257 students when he graduated in 2015. That is (0, 257)
In 2018, and his class has 329 students, That is (3, 329)
The linear equation is calculated using (0, 257) and (3, 329):
y - 257 = [(329 - 257)/(3 - 0)](x - 0)
y - 257 = 24x
y = 24x + 257
The linear equation is given as y = 24x + 257
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The midpoint of AB is M(6, 3) . If the coordinates of A are (7, 4) , what are the coordinates of B?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +7}{2}~~~ ,~~~ \cfrac{ y +4}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(6~~,~~3)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +7}{2}=6\implies x+7=12\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +4}{2}=3\implies y+4=6\implies \boxed{y=2}[/tex]
The following numbers represents the number of phone calls a class made in a given week:
125, 86, 142, 98, 126, 128, 90, 88, 98, 121
Use this data to find the following information. SHOW ALL WORK FOR CREDIT!
Mean: 110
e
Range:
Mode:
The mode and range of the given data is 98 and 42 respectively.
What is data?
Data, which can describe quantity, quality, fact, statistics, other fundamental units of meaning, or simply sequences of symbols that can be further interpreted, is a collection of discrete values that convey information in the pursuit of knowledge. A datum is a distinct state within a collection of data. Typically, data is arranged into structures like tables that give it additional context and meaning and can also be used as their own form of data in larger structures. It's possible to use data as variables in a computation. Data can represent both concrete measurements and abstract concepts. Data is used frequently in virtually every aspect of human organisational activity, including finance and science. Stock prices, crime rates, unemployment rates, literacy rates, and census data are a few examples of data sets.
Mode = 98 ( 98 occurs two times)
Range = 128-86=42
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A local car dealership is trying to sell all of the cars that are on the lot. Currently, there are 725 cars on the lot, and thegeneral manager estimates that they will consistently sell 50 cars per week.1. Write and solve an inequality that can be used to find the number of full weeks, w, it will take for the number ofcars to be fewer than 125. Since w is the number of full or complete weeks, w = 1 means at the end of week 1.
Number of cars in the lot = 725 cars
W is the number of full or complete weeks
Also, 50 cars per week = 50w;
For every week, the cars will be reducing by 50;
(A) Hence , the inequality is given as;
[tex]725-50w<125[/tex][tex]\begin{gathered} 725-125<50w \\ 600<50w \\ \frac{600}{50}12 \end{gathered}[/tex]Which has a greater value?
√8 + 3 or 8 + √3
Answer:
8 + √3 is greater.
Step-by-step explanation:
8 + √3 equals 9.73
whereas
√8 + 3 equals 5.83
If you mix 3 oz of blue paint with 2 oz of yellow paint, and then decide to create 20 oz of the same mixture, how many ounces of yellow paint do you need?
tata:
• Blue paint (,: B,) 3
,• ellow poaint (
,• Mixture obtained ( ),O
,• Total mixture (), T
,• Total yellow paint (): , TY
Proportion f Y:
[tex]Y=\frac{2}{5}=0.4[/tex]TY:
[tex]TY=Y\cdot T=0.4\cdot20=8oz[/tex]nswer: 8oz
ummary:
0. We got the proportion of yellow paint in the mixture
,1. We multiply the proportion by the total mixture to know how many ounces of yellow paint is needed.
the sum of two consecutive natural numbers is 313
Answer:
156 and 157
Step-by-step explanation:
if m(x)=x-7 and n(x)= 1/x+7 find the function value if possible of (mxn)(7)
The function value if possible of (mxn)(7) is mathematically given as
(m.n)(7) =0
This is further explained below.
What is the function value if possible of (mxn)(7)?Generally, the equation for the is mathematically given as
m(x) &=x-7
Therefore
[tex]n(x) = \frac{1}{x}+7[/tex]
(m * n)(x) = m(x) * n(x)
[tex]=(x-7) \cdot\left(\frac{1}{x}+7\right)[/tex]
(m * n)(7) = (7-7) * n(1/7 + 1)
(m.n)(7) =0
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In her notebook, Pia wrote these steps to construct a square inscribed in a circle:Use a compass and a straightedge to find chord LM, which is the perpendicular bisector of JK. Then, use a straightedge to draw the four chordsthat make up the square: JL, LK, KM, and MJ.Which instruction is Pia missing?
We want to draw chord LM such that it is a perpendicular bisector of line JK. The square would be drawn by joining lines JL, KL, KM and MJ
To achieve this, the daigram should look like the one shown below
This diagram is only possible if JK passes through the center of the circle. This means that JK is the diameter of the circle. Thus, the correct option is
B
Answer:
B
Step-by-step explanation:
10. Find the value of a²-b if a = 3 and b = -5.
please help with this
Answer:
supplementary, not congruent.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
74.44
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]
Jonah studied z hours for a big test. Francesca studied a fourth as long. Write an algebraic expression for long Francesca studied.
The expression for study hours of Francesca will be ( Z + 4 ) hours.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jonah studied z hours for a big test. Francesca studied a fourth as long as Jonah studied.
The expression will be written as Francesca studied 4 hours more than Jonah.
Francesca's study time = ( Z + 4 ) hours
Therefore, the expression for study hours of Francesca will be ( Z + 4 ) hours.
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Shandra owns a goldfish that currently weighs 0.50 ounces. With each inch that the goldfish grows, the goldfish weighs an additional0.15 ounces.PARTACreate an equation that Shandra can use to find the number of inches, r, it will take for the goldfish to weigh 1.1 ounces.PART BHow many more inches does the goldfish need to grow to weigh 1.1 ounces?inches
A.
The initial weight of the goldfish is 0.5 ounces.
Then, for each inch it grows, its weight increases by 0.15 ounces.
So, using the variable r to represent the number of inches it grew, we can write the following equation to determine the value of x for a weight of 1.1 ounces:
[tex]0.5+0.15r=1.1[/tex]B.
Solving the equation for r, we have:
[tex]\begin{gathered} 0.15r=1.1-0.5 \\ 0.15r=0.6 \\ r=\frac{0.6}{0.15} \\ r=4 \end{gathered}[/tex]It needs to grow 4 more inches.
is (-2, -6) a solution of y less than 7x + 8
Answer:
Not a solution.
Step-by-step explanation:
[tex]y < 7x+8\\-6 < 7(-2)+8\\-6 < -14 + 8\\-6 < -6; False[/tex]
This is not true because -6 is not less than -6.
Answer: No.
Step-by-step explanation: First of all you need to know that (x,y) x goes in front of y because of alphabetical order. Second, plug in your points (-2,-6) into your equation y < 7(-2) + 8. After you solve, you will get y < -14+8. Then, you get y < -6. On your point it said that -6 is your y point. Plug in -6 into y and you get -6 < -6. So no, y is not less than 7x +8. Hope this helps!
I need help on this problem can you help me?
The incenter is the center of a circumference that can be circumscribed inside the triangle. That means that the distance from the circumcenter to the sides of the triangle is the same. In this case, it means that:
[tex]NK=NL=NM[/tex]On the other hand, the segments from the circumcenter N to the vertices of the triangle are angle bisectors, and using that fact, it can be proven that the two triangles that form at each vertex from the angle bisectors are congruent. Then, we can also know that:
[tex]HK=HM[/tex]The congruence that cannot be deduced from the given information is:
[tex]NG\cong NJ[/tex]