Recall that the formula for the length of the diagonal of a rectangle is:
[tex]l=\sqrt[]{a^2+b^2}.[/tex]Where a, and b are the lengths of the sides of the rectangle.
Substituting a=161´, b=326´ in the above formula we get:
[tex]\begin{gathered} l=\sqrt[]{(161^{\prime})^2+(326^{\prime})^2}, \\ l=363.5890537^{\prime}\text{.} \end{gathered}[/tex]Answer: 363.5890537 ´.
20. You want to take your family on a two week vacation this summer, which is 5 months away The total cost for the vacation is $2,245. You work extra hours at your job at $11.25 per hour. Fifteen percent of your earnings go to taxes, and the rest goes toward the expenses for this vacation. Over next five months, what is the fewest number of extra hours per month you could work and still me enough money to take this vacation? A 35 ( C. 47 E.235 8.40 D. 200 AIS rregues stepl. In this ques we are given that guastotares family to go for at Vacation this summes need atat sum 15 Then, you need to hours at your sub this vacation
Assuming that all 5 months have 30 working days.
Let us assume that you need to do 'x' hours per month to get the extra money for vacation.
Given that overtime wage is $11.25 per hour, the wage (in $) for monthly overtime is obtained as,
[tex]\begin{gathered} \text{Monthly Overtime Wage}=\text{ Monthly overtime hours}\times\text{ Wage per hour} \\ \text{Monthly Overtime Wage}=x\times11.25 \\ \text{Monthly Overtime Wage}=11.25x \end{gathered}[/tex]Then the total amount (TA) earned in 5 months of overtime work is calculated as,
[tex]\begin{gathered} \text{ Total Amount}=\text{ Amount per month}\times\text{ No. of months} \\ \text{Total Amount}=11.25x\times5 \\ \text{Total Amount}=56.25x \end{gathered}[/tex]Given that the 15% of this amount earned goes for the tax, so the net amount earned is given by,
[tex]\begin{gathered} \text{Net Amount Earned}=(1-\frac{15}{100})\times56.25x \\ \text{Net Amount Earned}=(\frac{85}{100})\times56.25x \\ \text{Net Amount Earned}=47.8125x \end{gathered}[/tex]This net amount must be sufficient to cover the total cost of vacation $2245,
[tex]\begin{gathered} \text{ Net Amount Earned}=\text{ Expense on vacation} \\ 47.8125x=2245 \\ x=\frac{2245}{47.8125} \\ x=46.95 \\ x\approx47 \end{gathered}[/tex]Thus, you have to work 47 hours of overtime monthly to cover the cost of the vacation in 5 months.
Answer:
this guy is right
Step-by-step explanation:
Find the value of n.1 x 4 = n
n = 4
The value of n is 4
pls help i give brainliest
Answer: They bought 2 adult tickets and 3 children's tickets.
Step-by-step explanation: If you multiply the adult tickets, (5.10,) by 2, and then multiply the children's tickets (3.6), you will then add the products together. Your answer should come up as 21.00 dollars.
A veterinarian is enclosing a rectangular outdoor running area against his building for the dogs he cares for (see image). He wants to maximize the area using 108 feet of fencing.
ANSWER
The width that will give the maximum area is 27 feet. The maximum area is 1458 square feet.
EXPLANATION
The equation that gives the area is a quadratic function,
[tex]A(x)=x(108-2x)[/tex]To find the width that maximizes the area, we have to find the x-coordinate of the vertex of this parabola. We can observe in the equation that the leading coefficient is -2, so the vertex is the maximum.
First, apply the distributive property to write the equation in standard form,
[tex]A(x)=-2x^2+108x[/tex]The x-coordinate of the vertex of a parabola if the equation is in standard form is,
[tex]\begin{gathered} y=ax^2+bx+c \\ \\ x_{vertex}=\frac{-b}{2a} \end{gathered}[/tex]In this case, b = 108 and a = -2,
[tex]x_{vertex}=\frac{-108}{-2\cdot2}=\frac{108}{4}=27[/tex]Hence, the width that will give the maximum area is 27 feet.
To find the maximum area, we have to find A(27),
[tex]A(27)=27(108-2\cdot27)=27(108-54)=27\cdot54=1458[/tex]Hence, the maximum area is 1458 square feet.
Hello, I need help on the following question (it’s one problem but with multiple parts):
Part i. We are told that the cost for 3 throws is 1 dollar. This means that if "x" is the number of throws then the total cost must be:
[tex]C(x)=\frac{1\text{ dollar}}{3\text{ throws}}x[/tex]We can rewrite it in a simpler form as:
[tex]C(x)=\frac{1}{3}x[/tex]If we purchased the armband then this cost is equivalent to (1/6) of a dollar per throw plus the cost of the armband, we get:
[tex]C_2(x)=\frac{1}{6}x+10[/tex]Part ii. The graph of the two equations are two lines in the plane, like this:
In the graph, the red line represents the cost without the armband and the blue line represents the cost with the armband.
Part iii. We can see from the graph that if the number of throws is smaller than 60, then the cost is smaller without the armband, but if the cost is greater than 60 then the cost is smaller with the armband. Therefore, it makes sense to buy the armband if the number of throws is going to be greater than 60.
help me to complete this please help me help help help help help help help help
Hello
To solve this question, we just have to find 40% of 90
[tex]\begin{gathered} \frac{40}{100}=\frac{x}{90} \\ 0.4=\frac{x}{90} \\ x=90\times0.4 \\ x=36 \end{gathered}[/tex]From the calculations above, the castle has 36 girls present
Find the terminal point on the unit circle determined by 4pi/3 radians
Given:
A terminal point on the unit circle determined by 4pi/3 radians
The unit circle has a radius = 1
the terminal point (x,y) will be calculated using the following formulas:
[tex]\begin{gathered} x=cos(\theta) \\ y=sin(\theta) \end{gathered}[/tex]Substitute θ = 4pi/3
[tex]\begin{gathered} x=cos(\frac{4\pi}{3})=-\frac{1}{2} \\ \\ y=sin(\frac{4\pi}{3})=-\frac{\sqrt{3}}{2} \end{gathered}[/tex]So, the answer will be:
[tex](x,y)=(-\frac{1}{2},-\frac{\sqrt{3}}{2})[/tex]I have to write the equation in slope intercept form. i need help, please. thank you
step 1
find the slope
we have the points
(-6,10) and (-3,-2)
m=(-2-10)/(-3+6)
m=-12/3
m=-4
step 2
find the equation in point slope form
y-y1=m(x-x1)
we have
m=-4
(x1,y1)=(-6,10)
substitute
y-10=-4(x+6)
step 3
convert to slope intercept form
isolate the variable y
y-10=-4x-24
y=-4x-24+10
y=-4x-14
what will be the cost of material if the volume is 180in^3 and the surface area is 258in^2 and the cardboard cost $0.05 per square inch.cost of material is?
A material in the shape of a rectangular prism (cuboid) is given.
The volume and the surface area are given to be 180in³ and 258in², respectively. The cost of the material per square inch is given to be $0.05.
It is required to find the cost of the material.
To do this, since the cost per square inch is given, multiply the surface area by the cost per square inch:
[tex]258\times0.05=\$12.9[/tex]The cost of the material is $12.9.
Given P = 2L + 2W. Solve for W if P = 52 and L 18 W
First begin by making w the subject of formula
p = 2l + 2w
p-2l = 2w ( moving 2l to the left hand side )
[tex]\begin{gathered} \\ \frac{p\text{ - 2l}}{2}\text{ = w ( now we've made w the subject )} \end{gathered}[/tex]next substitute in your values p = 52 and l = 18
[tex]w\text{ = }\frac{p\text{ - 2l}}{2}\text{ = }\frac{52\text{ - 2(18)}}{2}\text{ = }\frac{52\text{ - 36}}{2}\text{ = }\frac{16}{2}\text{ = 8}[/tex]
Therefore the value for w in the expression is 8
Solve the equation. – 4y - 37 = 6y + 13 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. y= (Type an integer or a simplified fraction.) B. The solution is all real numbers. C./ There is no solution.
solve for y:
add 4y to both sides:
[tex]\begin{gathered} -4y-37+4y=6y+13+4y \\ -37=10y+13 \end{gathered}[/tex]Subtract 13 from both sides:
[tex]\begin{gathered} -37-13=10y+13-13 \\ -50=10y \end{gathered}[/tex]Divide both sides by 10:
[tex]\begin{gathered} \frac{10y}{10}=-\frac{50}{10} \\ y=-5 \end{gathered}[/tex]In the form (x+4)(x-2)=1, the zero-factor property can or cannot be used to solve equation?
The zero-factor property is
[tex](x+a)(x+b)=0[/tex]Then we equate each factor by 0 and find the values of x
The given equation is
[tex](x+4)(x-2)=1[/tex]Since the right side is not equal to 0, then
We can not use the zero-factor property to solve the equation
The answer is
zero-factor property cannot be used
Solve the system of equations.−2x+5y =−217x+2y =15
To solve this question we will use the elimination method.
Adding 7 times the first equation to 2 times the second equation we get:
[tex]14x+4y+(-14x)+35y=30+(-147)\text{.}[/tex]Simplifying the above equation we get:
[tex]4y+35y=-117.[/tex]Solving for y we get:
[tex]\begin{gathered} 39y=-117, \\ y=-\frac{117}{39}, \\ y=-3. \end{gathered}[/tex]Substituting y=-3 in the first equation, and solving for x we get:
[tex]\begin{gathered} -2x+5(-3)=-21, \\ -2x-15=-21, \\ -2x=-6, \\ x=3. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} x=3, \\ y=-3. \end{gathered}[/tex]Evaluate the equation: -9w = -54
Solution:
Given the equation:
[tex]-9w=-54[/tex]To solve for the unknown (w), we divide both sides of the equation by the coefficient of w.
The coefficient of w is -9.
Thus,
[tex]\begin{gathered} -\frac{9w}{-9}=-\frac{54}{-9} \\ \Rightarrow w=6 \end{gathered}[/tex]Hence, the value of w is
[tex]6[/tex]Plot the inequality on the given number line. Toggle the "Dot" or "Open Dot" button to place the correct dot on your line before you submit your answer.x<0Write the inequality using interval notation. Use "oo" (two lower case o's) for∞.
Answer:
(b) (-oo, 0)
Explanation:
Given the inequality:
[tex]x<0[/tex](a)The inequality is plotted on the number line below:
Note: An open circle is used for the inequalities, < and >.
(b)The inequality written using the interval notation is:
[tex](-\infty,0)[/tex]Find the center that eliminates the linear terms in the translation of 4x^2 - y^2 + 24x + 4y + 28 = 0.(-3, 2)(-3,- 2)(4, 0)
Step 1
Given;
[tex]4x^2-y^2+24x+4y+28=0[/tex]Required; To find the center that eliminates the linear terms
Step 2
[tex]\begin{gathered} 4x^2-y^2+24x+4y=-28 \\ 4x^2+24x-y^2+4y=-28 \\ Complete\text{ the square }; \\ 4x^2+24x \\ \text{use the form ax}^2+bx\text{ +c} \\ \text{where} \\ a=4 \\ b=24 \\ c=0 \end{gathered}[/tex][tex]\begin{gathered} consider\text{ the vertex }form\text{ of a }parabola \\ a(x+d)^2+e \\ d=\frac{b}{2a} \\ d=\frac{24}{2\times4} \\ d=\frac{24}{8} \\ d=3 \end{gathered}[/tex][tex]\begin{gathered} Find\text{ the value of e using }e=c-\frac{b^2}{4a} \\ e=0-\frac{24^2}{4\times4} \\ e=0-\frac{576}{16}=-36 \end{gathered}[/tex]Step 3
Substitute a,d,e into the vertex form
[tex]\begin{gathered} a(x+d)^2+e \\ 4(x+_{}3)^2-36 \end{gathered}[/tex][tex]\begin{gathered} 4(x+3)^2-36-y^2+4y=-28 \\ 4(x+3)^2-y^2+4y=\text{ -28+36} \\ \\ \end{gathered}[/tex]Step 4
Completing the square for -y²+4y
[tex]\begin{gathered} \text{use the form ax}^2+bx\text{ +c} \\ \text{where} \\ a=-1 \\ b=4 \\ c=0 \end{gathered}[/tex][tex]\begin{gathered} consider\text{ the vertex }form\text{ of a }parabola \\ a(x+d)^2+e \\ d=\frac{b}{2a} \\ d=\text{ }\frac{4}{2\times-1} \\ d=\frac{4}{-2} \\ d=-2 \end{gathered}[/tex][tex]\begin{gathered} Find\text{ the value of e using }e=c-\frac{b^2}{4a} \\ e=0-\frac{4^2}{4\times(-1)} \\ \\ e=0-\frac{16}{-4} \\ e=4 \end{gathered}[/tex]Step 5
Substitute a,d,e into the vertex form
[tex]\begin{gathered} a(y+d)^2+e \\ =-1(y+(-2))^2+4 \\ =-(y-2)^2+4 \end{gathered}[/tex]Step 6
[tex]\begin{gathered} 4(x+3)^2-y^2+4y=\text{ -28+36} \\ 4(x+3)^2-(y-2)^2+4=-28+36 \\ 4(x+3)^2-(y-2)^2=-28+36-4 \\ 4(x+3)^2-(y-2)^2=4 \\ \frac{4(x+3)^2}{4}-\frac{(y-2)^2}{4}=\frac{4}{4} \\ (x+3)^2-\frac{(y-2)^2}{2^2}=1 \end{gathered}[/tex]Step 7
[tex]\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \\ \text{This is the }form\text{ of a hyperbola.} \\ \text{From here } \\ a=1 \\ b=2 \\ k=2 \\ h=-3 \end{gathered}[/tex]Hence the answer is (-3,2)
what is the distance between A and B B(4,5) A(-3,-4)
11.40 units
Explanation
Step 1
you can easily find the distance between 2 points using:
[tex]\begin{gathered} d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ \text{where} \\ P1(x_1,y_1)\text{ and } \\ P2(x_2,y_2) \end{gathered}[/tex]Step 2
Let
A=P1(-3,-4)
B=P2(4,5)
Step 3
replace
[tex]\begin{gathered} d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ d=\sqrt[]{(5-(-4))^2+(4-(-3))^2} \\ d=\sqrt[]{(9)^2+(7)^2} \\ d=\sqrt[]{81+49} \\ d=\sqrt[]{130} \\ d=\text{11}.40 \end{gathered}[/tex]I hope this helps you
make a triangular garden in the backyard. you know that one side of your yard (ac) is 100 yards long and another side (ab) is 250 yards. in order for the garden to fit and not cross into the neighbor's yard, what must be the measure of angle b if angel c measures 95 degrees?
Law of sines for the given triangle:
[tex]\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]Use the equation above and the given data to solve angle B:
[tex]undefined[/tex]TIME SENSITIVE The first step in solving this equation is to (BLANK) the second step is to (BLANK) solving this equation for X initially yields (BLANK) checking solution shows that (BLANK= 0 and 2 are valid solutions)
Give
[tex](4x)^{\frac{1}{3}}-x=0[/tex]
Procedure
The first step in solving this equation is to add x to both sides
[tex](4x)^{\frac{1}{3}}=x[/tex]The second step is to cube both sides
[tex]4x=x^3[/tex]solving this equation for X initially yields in three solutions
[tex]\begin{gathered} x(4-x^2)=0 \\ x(2-x)(2+x)=0 \end{gathered}[/tex]checking solution shows that x = 0, x = -2 and x = 2
The height and weight of adults can be related by the equation y = 48.3x 127 where a is height in feet and y is weight in poundsWhat does the slope of the line represent?A. the number of pounds heavier an adult one foot taller would weighB. the height of an adult weighing zero poundsOC. the average number of pounds per foot tallD. the number of adults in the sampleReset SelectionviousNext
The slope of the line y = 48.3x - 127 represents the number of pounds heavier an adult one foot taller would weigh .
The given line is y = 48.3x - 127
So we can use this equation to find the weight of various people of different heights.
At x = 6 , y = 48.3 × 6 - 127 = 162.8 pounds
At x = 7 , y = 48.3 × 7 - 127 = 211.1 pounds
Difference of the two weights = 211.1 - 162.8 = 48.3
The slope of something like a line in the plane consisting of the x and y axes is typically denoted by the letter m. This slope is calculated by dividing the linear change in the y coordinate between two separate points on the line by the equivalent change in the x coordinate.
Hence the slope which is 48.3 represents the difference in height of people who are a feet taller.
To learn more about slope visit:
https://brainly.com/question/16941905
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The dot plot below shows 6 data points with the mean of 16What is the absolute deviation at 19?○3○4○7○8
we have that
The mean is 16
Find the difference between each data point and the mean
so
16-12=4
16-13=3
16-15=1
17-16=1
19-16=3
20-16=4
Find the average of these values
(4+3+1+1+3+4)/6
=16/6
=2.67
If Joey worked for himself and called his company “Joey’s Construction Company” and made $20,750 per year, how much would he pay per year in total Social Security and Medicare tax?
He would pay $3,154 in Social Security and Medicare tax
Explanation:Given that Joey worked for himself, he must pay doule the amount of Social Security and Medicare taxes to the government.
This makes 15.2% of $20,750
[tex]\begin{gathered} =\frac{15.2}{100}\times20750 \\ \\ =3154 \end{gathered}[/tex]He would pay $3,154 in total Social Security and Medicare tax
An isosceles triangle has an angle that measures 128°. Which other angles could be in that Isosceles triangle? Choose all that apply.
Given:
Given angle is 128 degree.
In Isosceles triangle two angles are equal.
Let the angle be x.
Sum of the angles in a triangle is 180 degree.
[tex]\begin{gathered} 128+x+x=180 \\ 2x=180-128 \\ 2x=52 \\ x=26^{\circ} \end{gathered}[/tex]Other angles in an Isosceles triangle is 26 degree.
2,-2,-6,-10,-14, ...how do I go about finding the explicit formula?
According to the given sequence, the difference is -4, because it's decreasing with that difference: 2-2 = -2; -2-4 = -6; and so on.
To find the explicit formula, we use the arithmetic sequence formula.
[tex]a_n=a_1+(n-1)d[/tex]Replacing all the given information, we have.
[tex]\begin{gathered} a_n=2+(n-1)\cdot(-4) \\ a_n=2-4n+4 \\ a_n=6-4n \end{gathered}[/tex]This explicit formula we can also express as
[tex]f(n)=6-4n[/tex]The sum of two numbers is at least 8, and the sum of one of the numbers and 3 times the second mumber isno more than 15.
As given by the question
There are given that the sum of the two numbers is at least 8.
Now,
Let the unknown numbers be x and y
Then,
If the sum of the two numbers is at least 8 then:
[tex]x+y\ge8[/tex]Similarly, the sum of one of the numbers and 3 times the second number is no more than 15
Then,
[tex]x+3y\leq15[/tex]Now,
From the both of the inequality:
[tex]\begin{gathered} x+y\ge8 \\ x+3y\leq15 \end{gathered}[/tex]Then, find the first and second nuber:
So,
[tex]\begin{gathered} x+y\ge8 \\ x\ge8-y\ldots(a) \end{gathered}[/tex]Then, Put the value of x into the second equation
Then,
[tex]\begin{gathered} x+3y\leq15 \\ 8-y+3y\leq15 \\ 8+2y\leq15 \\ 2y\leq15-8 \\ y\leq\frac{7}{2} \\ y\leq3.5 \end{gathered}[/tex]Then,
Put the value of y into the equation (a)
[tex]\begin{gathered} x\ge8-y \\ x\ge8-3.5 \\ x\ge4.5 \end{gathered}[/tex]Hence, the first number and second number is shown in below:
[tex]\begin{gathered} x\ge4.5 \\ y\leq3.5 \end{gathered}[/tex]The graph of the given result is shown below:
Find the difference. Express the answer in scientific notation.(4.56 times 10 Superscript negative 13 Baseline) minus (1.17 times 10 Superscript negative 13)3.39 times 10 Superscript negative 265.73 times 10 Superscript negative 263.39 times 10 Superscript negative 135.73 times 10 Superscript negative 13
Given:
given expression is
[tex](4.56\times10^{-13})-(1.17\times10^{-13})[/tex]Find:
we have to elavuate the difference and write the answer in scientific notation.
Explanation:
we will evaluate the expression as follows
[tex](4.56\times10^{-13})-(1.17\times10^{-13})=(4.56-1.17)\times10^{-13}=3.39\times10^{-13}[/tex]Therefore, correct option is
[tex]3.39\times10^{-13}[/tex]In 9-16, estimate each product. 9. 0.12 x 105 10. 45.3 x 4 11. 99.2 x 82 12. 37 x 0.93 13. 1.67 X4 14. 3.2 x 184 15. 12 x 0.37 16. 0.904 x 75
9.
[tex]\begin{gathered} 0.12\cdot105=12.6 \\ 10.\text{ 45.3}\cdot4=181.2 \\ 11.\text{ 99.2}\cdot82=8134.4 \\ 12.\text{ 37}\cdot0.93=34.41 \\ 13.\text{ 1.67}\cdot4=6.68 \\ 14.\text{ 3.2}\cdot184=588.8 \\ 15.\text{ 12}\cdot0.37=4.44 \\ 16.\text{ 0.904}\cdot75=67.8 \end{gathered}[/tex]What is the density, in grams/cubic inch, of a substance with a mass of 6 grams filling a rectangular box with dimensions 2 in x 6 in x 3 in?6 8 0.11 0.17
Consider tha the density is calculated by using the following formula:
[tex]D=\frac{M}{V}[/tex]D is the density, M is the mass and V the volume. In this case, you have;
M = 6 g
V = 2 in x 6 in x 3 in = 36 in^3
Replace the previous values of the parameters into the formula for D:
[tex]D=\frac{6g}{36in^3}\approx0.17\frac{g}{in^3}[/tex]Hence, the density of the given substance is approximately 0.17 g/in^3
If the equation 6X equals 84, what is the next step in the equation solving sequence?
Answer: We have to find the next solution step for the following equation:
[tex]6x=84[/tex]The solution steps are:
[tex]\begin{gathered} 6x=84 \\ \\ \text{ Divide both sides by 6} \\ \\ \frac{6x}{6}=\frac{84}{6}\Rightarrow x=\frac{84}{6}=14 \\ \\ x=14 \end{gathered}[/tex]find the average rate of change from x= -2 to x =1
We have the graph of a function of third grade and need to find the average rate of change between x=-2 and x=1.
We can see that:
[tex]\begin{gathered} \text{The rate of change is:} \\ \frac{dy}{dx} \\ \end{gathered}[/tex]So, the average between x=-2 and x=1 is:
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