The given equation,
[tex]y=0.5x+3[/tex]Comparing it with the slope intercept equation
[tex]y=mx+c[/tex]where m is the slope.
Thus the slope is m=0.5.
Find the value of x. 984 (149-x) 128 2x+4)
You have a pentagon. In order to determine the value of x for the given expression, of the measure of the angles, take into account that the sum of the interior angles of a pentagon is 540°.
Then, by using the given expressions you have:
(98) + (149 - x) + (2x + 4) + (114) + (128) = 540
To solve for x, proceed as follow:
(98) + (149 - x) + (2x + 4) + (114) + (128) = 540 eliminate parenthesis
98 + 149 - x + 2x + 4 + 114 + 128 = 540 simplify like terms left side
493 + x = 540 subtract 493 both sides
x = 540 - 493
x = 47
Hence, the value of x is x = 47
which one of these must be a correct congruence statement
Answer:
C. AB ≅ DE
Explanation:
If triangles ABC and DEF are similar, then the following holds:
[tex]\begin{gathered} \angle A\cong\angle D \\ \angle B\cong\angle E \\ \angle C\cong\angle F \end{gathered}[/tex]Likewise, the similar sides are:
[tex]\begin{gathered} AB\cong DE \\ AC\cong DF \\ BC\cong EF \end{gathered}[/tex]The correct choice is C.
your budget is $80.00 to buy new clothes.what us the maximum whole dollar amount that you can spend on clothes, (bearing in mind that you will also have to pay 7.5 sales tax.)
We are told that the maximum amount to spend is $80 and that there is a 7.5% sales tax. If N is the amount we are going to spend then we need to have into account that we need to add the 7.5% of N and that should be at least equal to $80.
[tex]N+\frac{7.5}{100}N=80[/tex]Now we need to solve for N, to do that we add like terms:
[tex]\begin{gathered} (1+\frac{7.5}{100})N=80 \\ \frac{107.5}{100}N=80 \end{gathered}[/tex]Now we multiply both sides by 100:
[tex]107.5N=8000[/tex]Now we divide by 107.5:
[tex]N=\frac{8000}{107.5}[/tex]Solving the operations:
[tex]N=74.4\cong74[/tex]Therefore, the maximum amount to spend is $74
In a recent survey of college-educated adults, 351 indicated that they regularly work more than 45hrs a week. If this represents 39% of those surveyed, how many people were in the survey?
Recall that the y% of x is given by the following expression:
[tex]x\cdot\frac{y}{100}\text{.}[/tex]Now, let S be the number of people that were in the survey, then, we know that 39% of S is 351, then we can set the following equation:
[tex]351=S\cdot\frac{39}{100}\text{.}[/tex]Multiplying the above equation by 100/39 we get:
[tex]\begin{gathered} 351\times\frac{100}{39}=S\cdot\frac{39}{100}\times\frac{100}{39}, \\ S=900. \end{gathered}[/tex]Answer: 900.
Can you provide an example of a number that is a perfect square
ANSWER
9
EXPLANATION
A perfect square is a number that can be expressed as the product of two equal integers.
For example, 9 is a perfect square because it can be expressed as the product 3 x 3 = 3² - which are two equal integers.
MAKE CONNECTIONSKatie is twice as old as her sister Mara. The sum of their ages is 24. Write a one-variable equation tosituation
Answer
3x = 24
Explanation
Let sister Maria's age be represented by x.
Katie is twice as old as her sister Mara
So Katie's age will be 2x.
If the sum of their ages is 24, it implies x + 2x =24
Therefore, a one-variable equation to the situation will be: 3x = 24
What is the coefficient and the constant of 5x+2-3x^2
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]need help with this
x=19 * sin(40)
x = 12.21
1) Since we have a right triangle and the opposite leg to angle 40º, then we can write the following trig ratio
[tex]\begin{gathered} \sin (40)=\frac{x}{19} \\ x=19\cdot\sin (40) \\ x=12.21296 \\ x\approx12.21 \end{gathered}[/tex]2) Then the equation for that is x= 19*sin(40) and the value of that leg is approximately 12.21 units
5 A carpenter charges $720 for 18 hours of work. She charges the same amount of money foreach hour of work.Which table shows the relationship between the amount of time the carpenter works andamount of money she charges?theACarpenter's ChargesсCarpenter's ChargesAmountAmount ofAmountChargedTime WorkedCharged(dollars)(hours)(dollars)80375512571759225Carpenter's ChargesAmountCharged(dollars)720720720720Amount ofTime Worked(hours)2416062408320Carpenter's ChargesAmountCharged(dollars)720738756774Amount ofTime Worked(hours)19202122DAmount ofTime Worked(hours)14151617
Given:
A carpenter charges for 18 hours=$720.
Find:
We have to find the table which represents correct relationship between hours and charges.
Explanation:
A carpenter charges for 18 hours=$720.
A carpenter charges for 1 hour = 720/18 = $40.
Therefore, the charges of the carpenter for each hour is $40.
So, option A is correct option.
anyone that knows about cos, tan, and csc please help!
An ice cream cone costs $3 plus 6% sales tax. How many ice creamcones can be purchased for $24270908
We know that
• Each ice cream costs $3.
,• Sales tax is 6%.
,• The total amount of money is $24.
Let's find the unit price including sales tax.
[tex]3+0.06(3)=3+0.18=3.18[/tex]So, each ice cream costs $3.18 with sales tax included. Now, we divide $242 by this price to get the total number of ice creams we can buy
[tex]\frac{24}{3.18}=7.5[/tex]Therefore, we can buy 7 ice creams.please help!!!!!!!!!!
plane flies 390 miles with the wind
or 325 miles against the wind
The speed of the wind is 10 miles per hour
find the speed of the plane
In this case, we can see that
[tex]\begin{gathered} \frac{390\text{ miles}}{x+10\text{ }}\text{ must be equal to } \\ \frac{325}{x-10} \end{gathered}[/tex]hence the answer is
[tex]\frac{390\text{ miles}}{x+10\text{ }}=\frac{325\text{ miles}}{x-10\text{ }}[/tex]Write the inequality shown by the shaded region in the graph with the boundary line 3x-y=9.
The equation given is,
[tex]3x-y=9[/tex]Since the boundary line is thick bold line and from the graph we can observe that the line (shaded portion) moves from the right to the left hand side.
Then the inequality of the shaded region is,
[tex]3x-y\leq9[/tex]which property of equality was used?3m + 14 = 193m + 14 - 14 = 19 - (19 - 5)
ANSWER
Subtraction property of equality
EXPLANATION
In this problem they subtracted 14 from both sides of the equation. On the left side we can see that subtraction clearly, but on the right side, we have (19-5). If we solve this: 19 - 5 = 14, we can see that 14 has been subtracted from the right side too.
Suppose that a certain fortunate person has a net worth of $76.0 billion ($ 7.60×1010 ). If her stock has a good year and gains $3.20 billion ( 3.20×109 ) in value, what is her new net worth? THE NEW NET WOTH IS 7.92×10^10 Suppose that this individual now decides to give one-eighth of a percent (0.125 % ) of her new net worth to charity. How many dollars are given to charity?
Find the 0.125% of 7.92x10^10: Multiply the amount by 0.125 and then divide into 100 or multiply the amount by 0.125/100
[tex]\begin{gathered} \frac{0.125}{100}=1.25\times10^{-3} \\ \\ 7.92\times10^{10}*1.25\times10^{-3}=(7.92*1.25)\times10^{10-3}=9.9\times10^7 \end{gathered}[/tex]Then, $9.9x10^7 are given to charityduring the election of the last president 120 srudents voted fir Lindsey and 280 of the students voted for Sharif. 400 students total voted. What percentage voted for Lindsey
From a total of 400 students ,
120 votes for Lindsey
280 votes for Sharif
then 200 students = 50%
. 100 students= 25%
. 20 students = (50%)/10 = 5%
then 120 students (100+20) belows to 25%+5%= 30%
30% students voted for Lindsey
Determine whether the following is a trinomial square.x² - 8x + 64-O NoYes
A trinomial square has two possible forms:
[tex]\begin{gathered} (a+b)^2=a^2+2ab+b^2 \\ (a-b)^2=a^2-2ab+b^2 \end{gathered}[/tex]So, for us to check if
[tex]x^2-8x+64[/tex]Is a trinomial square, we first check if the first and thrid terms are positive, because both options has positive first and thrid terms, even if a or b are negative, because they are squared in the process.
Both are positive, x² and 64.
Now, by comparison, we see that, in thi case we would have:
[tex]\begin{gathered} a=x \\ b^2=64 \\ b=8 \end{gathered}[/tex]If it is a trinomial square, than the middle term has to be:
[tex]-2ab[/tex]We use the negative form because we have a negative middle term.
So, let's see if it checks out:
[tex]-2ab=-2x\cdot8=-16x[/tex]We got -16x, but the middle term is -8x, they don't match.
Since they don't match, the given expression is not a trinomial square. The answer is No.
harlyne deposited $3400 into a savings account that has an annual simple interest rate of 0.2%. Find the amount in the savings account after each number of years.
2 years $
5 years $
8 years $
The simple interest after 2, 5 and 8 years on a principal of $3400 at 0.2% are $3413.6, $3434 and $3454.4 respectively
SIMPLE INTERESTSimple interest is a quick and easy method to calculate interest on the money, in the simple interest method interest always applies to the original principal amount, with the same rate of interest for every time cycle.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r(%) and is to be written as r/100.
Principal: The principal is the amount that initially borrowed from the bank or invested. The principal is denoted by P.Rate: Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be 5%, 10%, or 13%, etc. The rate of interest is denoted by R.Time: Time is the duration for which the principal amount is given to someone. Time is denoted by T.Amount: When a person takes a loan from a bank, he/she has to return the principal borrowed plus the interest amount, and this total returned is called Amount.Using the data given;
S.I = P × R × T
When T = 2 years
S.I = 3400 * 0.002 * 2
S.I = 13.6
The amount after 2 years = 3400 + 13. 6 = $3413.6
When T = 5 years
S.I = 3400 * 0.002 * 5
S.I = 34
The amount after 5 years = 34 + 3400 = $3434
When T = 8 years
S.I = $3454.4
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An object projected upwards with a velocity of 96 feet per second from a height of 6 feet above theground is modelled by the function ℎ() = −162 + 96 + 6 .A. [3 pts] How many seconds after launch will the object reach its maximum height? Round your answerto one decimal place.B. [3 pts] Find the maximum height that the object reaches. Round your answer to one decimal place.C. [3 pts] Find the x-intercept and explain its meaning on the context of the problem.D. [3 pts] After how many seconds will the object be 100 feet above the ground?E. [2 pts] Find the y-intercept and explain its meaning on the context of the problem
Given:
[tex]h(t)=-16t^2+96t+6[/tex]Find-:
(a) Maximum second after launch will the object reach its maximum height
(b) Find the maximum height that the object reaches.
(c) Find the x-intercept and explain its meaning in the context of the problem.
(d) After how many seconds will the object be 100 feet above the ground
(e) Find the y-intercept and explain its meaning on the context of the problem
Sol:
(a)
Maximum second after launch.
For maximum value derivative should be zero.
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h^{\prime}(t)=-(16\times2)t+96 \\ \\ \end{gathered}[/tex][tex]\begin{gathered} -32t+96=0 \\ \\ 32t=96 \\ \\ t=\frac{96}{32} \\ \\ t=3 \end{gathered}[/tex]After 3-second the object reaches maximum height.
(b)
For maximum height is at t = 3
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h(3)=-16(3)^2+96(3)+6 \\ \\ h(3)=(-16\times9)+(96\times3)+6 \\ \\ h(3)=-144+288+6 \\ \\ =150 \end{gathered}[/tex](c) x-intercept the value of y is zero that means:
[tex]\begin{gathered} h(t)=0 \\ \\ -16t^2+96t+6=0 \\ \\ -8t^2+48t+3=0 \\ \\ t=\frac{-48\pm\sqrt{48^2-4(-8)(3)}}{2(-8)} \\ \\ t=\frac{-48\pm48.98}{-16} \\ \\ t=6;t=-0.061 \end{gathered}[/tex]The negative value of "t" is not considered so at
x-intercept is 6 and -0.061
(d) Object be 100 feet above grounded is:
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ -16t^2+96t+6=100 \\ \\ -16t^2+96t-94=0 \\ \\ -8t^2+48t-47=0 \\ \end{gathered}[/tex]So, the time is:
[tex]\begin{gathered} t=\frac{-48\pm\sqrt{48^2-4(-8)(-47)}}{2(-8)} \\ \\ t=\frac{-48\pm\sqrt{800}}{-16} \\ \\ t=\frac{-48-28.28}{-16},t=\frac{-48+28.28}{-16} \\ \\ t=4.76,t=1.23 \end{gathered}[/tex]At t= 4.76 and t =1.23
(e)
For y-intercept value of "x" is zero.
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h(0)=-16(0)^2+96(0)+6 \\ \\ h(0)=6 \end{gathered}[/tex]So, the y-intercept is 6.
i need help with math Will u
The value of 'w' for the two parallel lines are cut by the transversal is 52.
What is meant by the supplementary angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two perspectives are known as supplements. When supplementary angles are combined, they form a straight angle (180 degrees). In other words, so unless Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary.For the given question
Two parallel lines are cut by the transversal.
Then,
w + (3w -28) = 180 (same side exterior angle of the traversal are supplementary)
Solve the equation;
4w - 28 = 180
4w = 208
w = 208/4
w = 52
Thus, the value of 'w' for the two parallel lines are cut by the transversal is 52.
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what is the value of x to the nearest tenth on problem 8
First let us define the theorem that would help us solve the problem
The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.
Next, applying the theorem:
[tex]4x\text{ - 9 = 15}[/tex]Solving for x:
[tex]\begin{gathered} Collect\text{ like terms} \\ 4x\text{ = 15 + 9} \\ 4x\text{ = 24} \\ Divide\text{ both sides by 4} \\ \frac{4x}{4}\text{ = }\frac{24}{4} \\ x\text{ = 6} \end{gathered}[/tex]Answer:
x = 6
Which part of the triangle do you feel most confident of identifying and why and How might you use a perpendicular bisector or an angle bisector in the everyday life.
Hello there. To solve this question, we have to remember some properties about triangles.
Given a triangle ABC as follows:
We can show for each point what it is on this triangle.
1. Midsegment. This is the segment that is parallel to the base, in this case BC and has half its length. Another property: it divides the sides AB and AC into proportional parts. See the drawing.
2. Circumcenter. Take the triangle and inscribe it in a circumference (all its vertices are in the circumference. Now take the perpendicular bisector of each sides. The point in which at least two of them intersects is the circumcenter. See the drawing.
3. Incenter. Take the bisectors of the angles of ABC. The point in which they intersect is the incenter. Another property: It is the center of the inscribed circumference that is tangent to all sides of the triangle.
2(-6+-3)to the power of 2 - (-6+-4)
To solve this expression we need to solve the parenthesis first:
[tex]\begin{gathered} 2(-9)^{2-(-10)} \\ 2(-9)^{2+10} \\ 2(-9)^{12} \\ 2(282429536481)=564859072962 \\ \end{gathered}[/tex]Hello not homework just review not worth any points question 9
We were given:
[tex]\begin{gathered} 74Dyani's age is not an even number. That means that:[tex]\begin{gathered} d=13\text{ or }15\text{ or }17 \\ \text{Dyani's age is the median} \\ \Rightarrow d=15 \\ \\ d=15 \end{gathered}[/tex]Dyani's age is halfway between Rachel & Shannon's:
[tex]\begin{gathered} d=\frac{r+s}{2} \\ 2d=c \\ 2(15)=r+s \\ 30=r+s \\ r+s=30 \\ \text{From the age set},\text{ the possible age of Rachel \& Shannon is 17 \& 13} \\ We\text{ were told that:} \\ sWe were given the inequality:[tex]\begin{gathered} sTherefore, the age of the girls are listed below:Shannon is 13 years old,
Mercedes is 14 years old
Dyani is 15 years old
Aisha is 16 years old
Rachel is 17 years old
24. Cree la gráfica aproximada de la función cuadrática con intersecciones en x en (-5, 0) y (3,0) y una intersección en y en (0, -7.5). 1. Seleccione un botón para elegir el tipo de gráfico. 2. Arrastre los dos puntos a la posición correcta.
Find the length of FG, Express your answer as a fraction times pie.
Given:
EF = 2
m∠FEG = 144 degrees.
Let's fid the length of arc FG.
To find the length of arc FG, apply the formula:
[tex]L=2\pi r\times\frac{\theta}{360}[/tex]Where:
r is the radius = 2
θ is the central angle = 144 degrees.
Thus, we have:
[tex]\begin{gathered} L=2\pi\times2\times\frac{144}{360} \\ \\ L=4\pi\times\frac{2}{5} \\ \\ L=\frac{8}{5}\pi\text{ } \end{gathered}[/tex]Therefore, the length of arc FG as a fraction times pi is:
[tex]\frac{8}{5}\pi[/tex]ANSWER:
[tex]\frac{8}{5}\pi[/tex]1. Smoesnail crawls at 3/25 m.p.h. At this rate, how far can he get in 1 2/3 hours?
Answer:
[tex]\frac{1}{5}\text{ miles}[/tex]Explanation:
Here, we want to get the distance the snail can go in the given time
Mathematically, we have it that:
[tex]\text{Distance = sp}eed\text{ }\times\text{ time}[/tex]speed = 3/25 mph
Time = 1 2/3 hours = 5/3 hours
Thus, we have it that:
[tex]\text{Distance = }\frac{3}{25}\text{ }\times\frac{5}{3}\text{ = }\frac{1}{5}\text{ miles}[/tex]At the North Carolina Zoo there is a bucket that contains food for the gorillas and the grizzly bears. The gorilla food weighs 5.384 kg. The gorilla food weighs 0.796 kg more than the grizzly bear food. How much food for both gorillas and grizzly bears are in the bucket?
The food for both gorilla and grizzly bear in the bucket is 9.972 kg.
Given, at the North Carolina Zoo there is a bucket that contains food for the gorillas and the grizzly bears.
The gorilla food weighs 5.384 kg. The gorilla food weighs 0.796 kg more than the grizzly bear food.
Let the weight of the grizzly bear food be x,
According to the question,
weight of gorilla food = weight of grizzly bear food + 0.796 kg
5.384 = x + 0.796
x = 5.384 - 0.796
x = 4.588
So, the food for both gorilla and grizzly bear in the bucket is 9.972 kg.
Hence, the food for both gorilla and grizzly bear in the bucket is 9.972 kg.
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6. A right triangle has legs of 4 and 5. What is the hypotenuse? Show your work.
Given:
The leg of 4 and 5
Find-:
The value of the hypotenuse
Explanation-:
The right triangle is:
Let the Hypotenuse is "x."
Use Pythagores theorm is:
[tex]\text{ Hypotenuse}^2=(\text{ Leg}_1)^2+(\text{ Leg}_2)^2[/tex]So the value of "x" is:
[tex]\begin{gathered} x^2=4^2+5^2 \\ \\ x^2=16+25 \\ \\ x^2=41 \\ \\ x=\sqrt{41} \end{gathered}[/tex]So value of hypotenuse is:
[tex]\begin{gathered} =\sqrt{41} \\ \\ \approx6.403 \end{gathered}[/tex]Use the Venn diagram shown to answer the question below.Which regions represent set B?
Answer
From the image attached, we can see that the regions in set B include
II
III
V
VI
Explanation
We are provided with the Venn Diagram for this question and asked to list the region spanned by set B.
For that, we will look at the circle representing the set B and easily list out the regions that exist in this circle.
From the image attached, we can see that the regions in set B include
II
III
V
VI
Hope this Helps!!!