Answer:
[tex]X=13\frac{3}{4}[/tex]Explanation:
Given the equation:
[tex]\frac{11}{16}=\frac{X}{20}[/tex]Multiply both sides of the equation by 20.
[tex]\begin{gathered} \frac{11}{16}\times20=\frac{X}{20}\times20 \\ \implies X=\frac{11\times20}{16} \end{gathered}[/tex]The result is obtained below:
[tex]\begin{gathered} X=\frac{11\times5\times4}{4\times4} \\ \text{ Cancel out one of the 4's.} \\ X=\frac{11\times5}{4} \\ X=\frac{55}{4} \\ X=13\frac{3}{4} \end{gathered}[/tex]The solution to the equation, X is 13 3/4.
Larry Mitchell invested $16,000 advance at 7% annual simple interest and the rest at 2% annual simple interest if his total yearly interest from both accounts was $920 find the amount invested at each rate
To solve this question we have to set and solve a system of equations.
Let S be the amount (in dollars) that Larry Mitchell invested in the 7% account, and T be the amount (in dollars) that he invested in the 2% account, then we can set the following system of equations:
[tex]\begin{gathered} S+T=16000, \\ 0.07S+0.02T=920. \end{gathered}[/tex]Solving the first equation for T we get:
[tex]T=16000-S\text{.}[/tex]Substituting T=16000-S in the second equation we get:
[tex]0.07S+0.02(16000-S)=920.[/tex]Applying the distributive property we get:
[tex]0.07S+320-0.02S=920.[/tex]Adding like terms we get:
[tex]0.05S+320=920.[/tex]Subtracting 320 from the above equation we get:
[tex]\begin{gathered} 0.05S+320-320=920-320, \\ 0.05S=600. \end{gathered}[/tex]Now, dividing by 0.05 we get:
[tex]\begin{gathered} \frac{0.05S}{0.05}=\frac{600}{0.05}, \\ S=12000. \end{gathered}[/tex]Finally, substituting S=12000 in T=16000-S we get:
[tex]\begin{gathered} T=16000-12000, \\ T=4000. \end{gathered}[/tex]Therefore, Larry invested $12,000 in the 7% account and $4,000 in the 2% account.
Answer: Larry invested $12,000 in the 7% account and $4,000 in the 2% account.
I need help on this problem. m/np^2=kplease help me with the steps
Answer
n = (m/p²k)
Explanation
We are told to solve for n, that is, make n the subject of formula.
[tex]\frac{m}{np^2}=k[/tex]To solve this, we first cross multiply
[tex]\begin{gathered} \frac{m}{np^2}=k \\ np^2\times k=m \\ np^2k=m \end{gathered}[/tex]np²k = m
Divide both sides by p²k
[tex]\begin{gathered} \frac{np^2k}{p^2k}=\frac{m}{p^2k} \\ n=\frac{m}{p^{2}k} \end{gathered}[/tex]Hope this Helps!!!
Which of the following represents z equals negative 4 radical 3 end radical plus 4 times i in trigonometric form?
Notice that
[tex]\begin{gathered} z=-4\sqrt[]{3}+4i=8(-\frac{\sqrt[]{3}}{2}+\frac{1}{2}i) \\ \Rightarrow z=8(-\frac{\sqrt[]{3}}{2}+\frac{1}{2}i) \end{gathered}[/tex]Set,
[tex]\begin{gathered} z=8(\cos x+i\sin x) \\ \Rightarrow8(\cos x+i\sin x)=8(-\frac{\sqrt[]{3}}{2}+\frac{1}{2}i) \\ \Rightarrow\cos x=-\frac{\sqrt[]{3}}{2},\sin x=\frac{1}{2} \end{gathered}[/tex]Then, angle x is in the second quadrant since cosx is negative and sinx is positive-
On the other hand,
Therefore, using the unitary circle,
Therefore, the angle that produces such values for the cosine and sine function is x=150°; thus,
[tex]\begin{gathered} x=150\degree \\ \Rightarrow z=8(-\frac{\sqrt[]{3}}{2}+\frac{1}{2}i)=8(\cos (150\degree+i\sin (150\degree))) \\ \Rightarrow z=8(\cos (150\degree+i\sin (150\degree))) \end{gathered}[/tex]The answer is option 4 (top to bottom)
A recipe calls for 2 cups of flour. Lee has only a 3-cup measuring cup. How many 3-cup measuring cups of flour does she need?
Answer: 2
Explanation:
With the 2cup measauring cup, Lee can measure cups in multiples of 2:
2, 4, 6, 8,...
And with the 3cup measuring cup, Lee can measure cups in multiples of 3:
3, 6, 9, 12,...
As we can see the common number is that both can measure 6 cups. (this is the minimum common multiple).
Lee neds 2 measuring cups of 3 cups. This is so that Lee can measure 6 cups of flour wich is a multiple of the 2 cups of flour that the recipe needs.
This is the clearest photo i can getDetermine the equation of the circle graphed below
Given the graph of the circle
To write the equation of the circle , we need to find the radius and the coordinates of the center
As shown in the figure :
The center of the circle = (h,k) = ( 7 , 5 )
And the radius of the circle = r = 3
The general equation of the circle is :
[tex](x-h)^2+(y-k)^2=r^2[/tex]Substitute with the values of h, k and r :
So, the equation of the given circle is :
[tex]\begin{gathered} (x-7)^2+(y-5)^2=3^2 \\ \\ (x-7)^2+(y-5)^2=9 \end{gathered}[/tex]How to find percentages in numbers?
Percentages are expressed in terms of 100. The symbol is %. Assuming the total number of oranges shared among 2 boys is 60. If one boy gets 40 oranges, the percentage of the total orange that the boy got would be expressed as
40/60 * 100 = 66.67%
The percentage is calculated with respect to the total.
Again, we can express a given number in terms of percentage. If we want to express 3/4 in terms of percentage, it becomes
3/4 * 100 = 75%
When does ball 2 reach the ground? round to the nearest hundredth.
Solution:
Given the function:
[tex]\begin{gathered} f(t)=-16t^2+h---\text{ equation 1} \\ where \\ f(t)\Rightarrow current\text{v height} \\ t\Rightarrow time \\ h\Rightarrow height \end{gathered}[/tex]When ball 2 reaches the ground, we have
[tex]f(t)=0----\text{ equation 2}[/tex]By substitution, we have
[tex]\begin{gathered} 0=-16t^2+h \\ add\text{ -h to both sides of the equation} \\ 0-h=-16t^2+h-h \\ \Rightarrow-h=-16t^2 \\ \therefore \\ t^2=\frac{h}{16}---\text{ equation 3} \end{gathered}[/tex]To find the time ball 2 reaches the ground, we have
[tex]\begin{gathered} From\text{ equation 3,} \\ t^2=\frac{h}{16} \\ but\text{ h = 277} \\ t^2=\frac{277}{16} \\ take\text{ the square root of both sides} \\ \sqrt{t^2}=\sqrt{\frac{277}{16}} \\ t=\pm4.16082 \\ but\text{ t cannot be negative.} \\ \therefore \\ t\approx4.16\text{ \lparen nearest hundredth\rparen} \end{gathered}[/tex]Hence, ball 2 reaches the ground at
[tex]t=4.16[/tex]
The 10th term of an A.P is double the 2nd term Find the 8th term, given that the first term is 7
Step 1
The nth term of an A.P is given as;
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ a_1=7 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} a_2=7+(2-1)d \\ a_2=7+d \\ a_{10}=2(7+d)=14+2d \\ a_{10}=7+9d \\ 7+9d=14+2d \\ 7d=7 \\ d=1 \end{gathered}[/tex]Hence the 8th term will be;
[tex]\begin{gathered} a_8=7+(8-1)d \\ a_8=7+7(1) \\ a_8=14 \end{gathered}[/tex]Can you please help me
In order to find the area of the trapezoid, consider the figure as formed by two right triangles with the same area, and one rectangle.
Then, if A1 is the area of one triangle and A2 is the area of the rectangle, you have for the area of the trapezoid:
A = 2A1 + A2
where, for the triangle you have:
A1 = b·h/2
b = (16 ft - 6ft)/2 = 5 ft
h = 12 ft
A1 = (5 ft)(12 ft)/2 = 30 ft²
and for the rectangle:
A2 = w·h
w = 6 ft
h = 12 ft
A2 = (6 ft)(12 ft) = 72 ft²
next, replace the values of A1 and A2 to get the area of the trapezoid:
A = 2(30 ft²) + 72 ft²
A = 60 ft² + 72 ft²
A = 132 ft²
Hence, the area of the given trapezoid is 132 ft²
the following is a figure of the trapezoid as formed by two triangle and one rectangle:
I you could just give me the answer that would be great no explanation needed:) I will give you a highesr rating if you do thank you
The correct answer is:
C) Dilation with respect to the origin by a scale factor of 2 followed by a traslation of 2 units left
Find each absolute value. A. 1-41 B. 101 C. 31 Drag the point on the number line. O units 100 150 50 -250 -200 -150 -100 -50 oo" powered by desmos
EXPLANATION:
A.The absolute value of a number is the same number regardless of its sign, in this case the absolute value of -4 is 4,because the distance from zero to number 4 remains 4 regardless of the sign it has is positive or negative.
B.The absolute value of zero is the same zero, and as the opposite of a number it has the same absolute value, but the opposite sign. The opposite of the number 0 will always be 0.,
C.The absolute value of 3 is the same as 3, and this is equivalent to the distance from zero to the number 3 regardless of the sign it has is positive or negative.
you have saved up $52 by earning $4 for each lawn you mow how many more lawns do you need to mow to reach a total of $74
Given:
Amount saved = $52
Amount you earn on each lawn = $4
Let's find how many more lawns you need to mow to reach a total of $74.
Let x represent number of lawns needed to reach a total of $74
We have the equation:
[tex]x=\frac{74-52}{4}[/tex]Let's solve for x:
[tex]\begin{gathered} x=\frac{74-52}{4} \\ \\ x=\frac{22}{4} \\ \\ x=5.5\approx6 \end{gathered}[/tex]Therefore, you need to mow 5.5 lawns which is approximately 6 lawns to reach a total of $74
Evaluate the following expression 10 + 4(6 - 2)
we are given the following expression:
[tex]10+4\mleft(6-2\mright)[/tex]To solve this expression we will first use the distributive property in the parenthesis, like this:
[tex]10+4\times6-4\times2[/tex]Solving the operations:
[tex]10+24-8[/tex]Now we solve the subtraction:
[tex]10+16[/tex]Now we solve the addition:
[tex]26[/tex]Therefore, the answer is 26.
The equation y= 2x + 7 represents the North Path on a map. a. Find the equation for a path that passes through the point (6, 3) and is parallel to the North Path. b. Find the equation for a path that passes through the same point but is perpendicular to North Path.
The equation y= 2x + 7 represents the North Path on a map.
a. Find the equation for a path that passes through the point (6, 3) and is parallel to the North Path.
b. Find the equation for a path that passes through the same point but is perpendicular to North Path.
we know that
the slope of the given equation is m=2
step 1
Find the equation for a path that passes through the point (6, 3) and is parallel to the North Path.
If two lines are parallel, then their slopes are equal
that means
the slope of the parallel line is m=2
Find the equation in slope intercept form
y=mx+b
we have
m=2
point (6,3)
substitute
3=2(6)+b
solve for b
3=12+b
b=-9
the equation is
y=2x-9step 2
Find the equation for a path that passes through the same point but is perpendicular to North Path.
If two lines are perpendicular, then their slopes are opposite reciprocal
so
the slope of the perpendicular line is m=-1/2
Find the equation of teh line in slope intercept form
y=mx+b
we have
m=-1/2
point (6,3)
substitute
3=(-1/2)(6)+b
3=-3+b
b=6
therefore
the equation is
y=(-1/2)x+6solve the system of linear equations by graphingy = 2x4x - y = 4
If we graph the two equations given, the solution will be the point of intersection of the graph.
The graph of the equations like the following.
We see that the point of intersection is (2, 4) which is our solution.
help please I need help
Input Data
Jacob has 96 books
Each shelf can hold 9 books
Procedure
# Shelves = 96 books / 9 books per shelf
# Shelves = 10.66
Rounding
#Shelves = 11
Can you please help me with the second and third problem they are really hard and im struggling to solve them
Given:
Tameka made x 2 points shots and y 3 points shots.
To find:
a) The expression that represents the total number of points.
b) Calculate points when x = 5 and y = 2.
Explanation:
a) The total number of points can be calculated as follows,
[tex]T=2x+3y[/tex]Where T represents the total number of points.
b) Substituting x = 5 and y = 2, we get
[tex]\begin{gathered} T=2(5)+3(2) \\ T=10+6 \\ T=16 \end{gathered}[/tex]So, the total number of points she got is 16 points.
Final answer:
The expression that represents the total number of points is,
[tex]T=2x+3y[/tex]The total number of points she got is 16 points.
y - 5 = –2(x + 1)Find the slope!
We are given the following equation
[tex]y-5=-2(x+1)[/tex]We want to find out the slope of the equation.
First of all, convert the given equation into slope-intercept form.
[tex]\begin{gathered} y-5=-2(x+1) \\ y-5=-2x-2 \\ y=-2x-2+5 \\ y=-2x+3 \end{gathered}[/tex]Recall that the standard slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope
b is the y-intercept
So comparing the standard form with the above equation,
The slope of the equation is
m = -2
The y-intercept is 3.
[tex]m=-2[/tex]What is the scale factor used in the enlargement from drawing 1 to draining 2(Express as a percent or a decimal)
The length of drawing 1 is 1.5 inches
Drawing 2 is 1.8 inches
We need to use the same side
Take Drawing 2 over drawing 1
1.8/1.5
1.2
The scale factor is 1.2
which expression would match the following situation? the maximum amount of people allowed in one class is 15
let
s = number of people allowed in the class
Therefore,
[tex]s\leq15[/tex]it wont let me load the image in . Create a box plot with the following data:574, 526, 512, 579, 595, 517, 524, 552, 558, 541
Step 1
Given; 574, 526, 512, 579, 595, 517, 524, 552, 558, 541
Required; To create a box plot
Step 2
Arrange in ascending order
[tex]512,\:517,\:524,\:526,\:541,\:552,\:558,\:574,\:579,\:595[/tex]Find the lower quartile
[tex]\begin{gathered} \mathrm{The\:first\:quartile\:is\:computed\:by\:taking\:the\:median\:of\:the\:lower\:half\:of\:a\:sorted\:set.} \\ 524 \end{gathered}[/tex]Find the upper quartile
[tex]\begin{gathered} The\:third\:quartile\:is\:computed\:by\:taking\:the\:median\:of\:the\:higher\:half\:of\:a\:sorted\:set \\ 574 \end{gathered}[/tex]The median is the middle number of the entire data
[tex]=\frac{541+552}{2}=546.5[/tex]The maximum and minimum values are;
[tex]595\text{ and 512 respectively}[/tex]Paulo lives 5 blocks west of Tina. Mason live 3 blocks east of Tina. How many blocks apart do Paulo and Mason live? Use subtraction to find the answer. Show your work.
if Paulo is five blocks from Tina's west. 3 blocks to Tina's east is Mason's home. Paulo and Mason thus live 2 blocks away from one another.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Paulo lives 5 blocks west of Tina. Mason lives 3 blocks east of Tina.
In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.
The number of blocks apart Paulo and Mason live is,
=5 - 3
=2 block
Thus, if Paulo is five blocks from Tina's west. 3 blocks to Tina's east is Mason's home. Paulo and Mason thus live 2 blocks away from one another.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ1
Suppose that the functions f and g are defined as follows F(x)=x-1 g(x)=x-1/x-4Find f/g then give its domain using an interval or union of intervals Simplify your answer as much as possible (f/g)(x)=Domain of f/g:
We have:
[tex]\begin{gathered} f(x)=x-1 \\ g(x)=\frac{x-1}{x-4} \end{gathered}[/tex]And we must find the quotient f/g. So let's take f and divide it by g:
[tex]\begin{gathered} \frac{f}{g}(x)=\frac{f(x)}{g(x)}=\frac{x-1}{\frac{x-1}{x-4}}=(x-1)\cdot\frac{x-4}{x-1}=x-4 \\ \frac{f}{g}(x)=x-4 \end{gathered}[/tex]So the result is x-4. In order to calculate its domain we must take into acount that it was made from dividing f by g so this isn't a simple linear function with a domain from negative infinite to positive infinite. Any number that isn't part of the domain of g or that makes g=0 is a number that doesn't belong to the domain of f/g either. Values that aren't part of the domain of g are those who make its divider equal to 0 so we have:
[tex]\begin{gathered} x-4=0 \\ x=4 \end{gathered}[/tex]The values that make g=0 are those which make its dividend equal to 0:
[tex]\begin{gathered} x-1=0 \\ x=1 \end{gathered}[/tex]All these calculation mean that the values 1 and 4 are not part of f/g domain. Then the domain can be written as:
[tex]\text{Dom}=(-\infty,1)\cup(1,4)\cup(4,\infty)[/tex]what is the inverse of the function y=2 log ^3 x
Given the following function:
[tex]y=2\log ^3\text{ x}[/tex][tex]\begin{gathered} y=2\log ^3\text{ x} \\ x=2\log ^3(y) \\ x=2\log ^3=3^{\frac{x}{2}} \\ =3^{\frac{x}{2}} \end{gathered}[/tex](If it isn't the given function in the question please feel free to reopen a new session, wasn't able to confirm with you on the function)
The store is selling a shirt that costs $32. You have a couponfor 10% off. How much will the shirt cost after you use thecoupon?
The cost of the shirt = $32
Reduction percentage = 10%
Therefore, the reduction is,
[tex]\frac{10}{100}\times32=3.2[/tex]The cost of the shirt is
[tex]32-3.2=28.8[/tex]The cost of the shirt after using the coupon is $ 28.8.
A soccer field is 50 yd wide and 60 yd long. Find the length of the diagonal ofsuch a field. Give an exact answer as a radical expression and an approximationto three decimal places.
A soccer field has a rectangular figure, this means, the sides of a rectangle form a right triangle with the diagonal, where the diagonal is the hypotenuse. To find the length of a hypotenuse when we know the legs, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that the sum of the square of the legs is equal to the square of the hypotenuse. If we call our diagonal as x, applying this theorem to our problem we have
[tex]50^2+60^2=x^2[/tex]Solving for x:
[tex]\begin{gathered} 50^2+60^2=x^2 \\ 2500+3600=x^2 \\ 6100=x^2 \\ x=\sqrt[]{6100} \\ x=10\sqrt[]{61} \\ x\approx78.102 \end{gathered}[/tex]Find the distance between the two pony in simplest radical form (-9,3) and (-3,-5)
Given the points ( -9 , 3 ) and ( -3 , -5 )
And we need to the distance between them
The formula to find the distance d is :
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]so, the distance =
[tex]\begin{gathered} d=\sqrt[]{(-3-(-9))^2+(-5-3)^2} \\ d=\sqrt[]{(-3+9)^2+(-5-3)^2} \\ d=\sqrt[]{6^2+(-8)^2} \\ d=\sqrt[]{36+64}=\sqrt[]{100} \\ d=10 \end{gathered}[/tex]so, the distance = 10
Evaluate the function f when we have at the indicated values.f(x)=-5x^2+2x-1f(-3)=Answerf(2)=Answer
The given function is expressed as
f(x) = - 5x^2 + 2x - 1
To find f(- 3), we would substitute x = - 3 into the function. We have
f(- 3) = - 5(- 3)^2 + 2(- 3) - 1 = - 45 - 6 - 1
f(- 3) = - 52
To find f(2), we would substitute x = 2 into the function. We have
f(2) = - 5(2)^2 + 2(2) - 1 = - 20 + 4 -1
f(2) = - 17
The answers are
f(- 3) = - 52
Find the value of x. Then select the correct set of angle measures for this triangle.
ANSWER
B. 31°, 106°, and 43°
EXPLANATION
First, we have to find the value of x. Knowing that the sum of the measures of all the interior angles of a triangle is 180°, we can write an equation for x,
[tex](5x-7)+(11x-4)+(3x+1)=180[/tex]Add like terms,
[tex]\begin{gathered} (5x+11x+3x)+(-7-4+1)=180 \\ \\ 19x-10=180 \end{gathered}[/tex]Add 10 to both sides,
[tex]\begin{gathered} 19x-10+10=180+10 \\ \\ 19x=190 \end{gathered}[/tex]And divide both sides by 19,1
[tex]\begin{gathered} \frac{19x}{19}=\frac{190}{19} \\ \\ x=10 \end{gathered}[/tex]Now, replace the value of x = 10 in the expressions for each angle's measure to find their values,
[tex]\begin{cases}5x-7=5\cdot10-7=50-7=43 \\ {11x-4=11\cdot10-4=110-4=106} \\ {3x+1=3\cdot10+1=30+1=31}\end{cases}[/tex]Hence, the set of angle measures for this triangle is 31°, 106°, and 43°.
Express as an inequality. Then graph the solution to the compound inequality and write the solution in interval notation. A can of soda is not properly filled if the amount of soda x in the can is more than 12.1 ounces or fewer than 11.6 ounces
Let 'x' be the amount of soda in the can.
The first condition can be written like this:
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