The given points are
(352, 150)
(352, 175)
(456, 150)
(456, 175)
Each point represents one vertex of the rectangle.
The points that have the same x-coordinate are in the same vertical line, this means that the diference between the y-coordinates of the point determine the length of the width of the rectangle.
Since is a rectangle both vertical sides are equal.
Using the points
(352, 150)
(352, 175)
You can calculate the width as:
[tex]\begin{gathered} w=y_2-y_1 \\ w=175-150 \\ w=25\text{units} \end{gathered}[/tex]The points that have the same y-coordinate are in the same horizontal line, if you calculate the difference between the x-coordinates of said points, you can determine the length of the rectangle.
Using the points
(456, 150)
(352, 150)
You can calculate the length as
[tex]\begin{gathered} l=x_2-x_1 \\ l=456-352 \\ l=104\text{units} \end{gathered}[/tex]So the rectangle has a length of 104 and a width of 25. Using these values you can calculate the area:
[tex]\begin{gathered} A=wl \\ A=25\cdot104 \\ A=2600\text{units}^2 \end{gathered}[/tex]What is the mean absolute deviation (MAD) of the dada set? 2, 5, 6, 12, 15 Enter your answer as a decimal in the box.
To get the mean absolute deviation, we first need the mean of the set. The mean is calculated by the sum of the values divided by the number of data:
[tex]\begin{gathered} \mu=\frac{2+5+6+12+15}{5} \\ \mu=\frac{40}{5} \\ \mu=8 \end{gathered}[/tex]To get the means absolute deviation, we have to get the absolute difference between each data and the mean, sum them up and divide by the number of data:
[tex]\begin{gathered} d_1=|2-8|=|-6|=6 \\ d_2=|5-8|=|-3|=3 \\ d_3=|6-8|=|-2|=2 \\ d_4=|12-8|=|4|=4 \\ d_5=|15-8|=|7|=7 \\ MAD=\frac{6+3+2+4+7}{5}=\frac{22}{5}=4.4 \end{gathered}[/tex]how do i solve for d ?3(2d-4) = 6(d-2)
Solution:
Given the equation;
[tex]3(2d-4)=6(d-2)[/tex]SImplify:
[tex]6d-12=6d-12[/tex]Since the two sides of the equation are equal, d has infinitely many solutions.
find the total and the interestprincipal $3200rate 5 1/2 yearscompounded semiannually for 6 years
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$3,200
r=5 1/2 %=5.5%=0.055
t=6 years
n=2
substitute the given values
[tex]A=3,200(1+\frac{0.055}{2})^{2\cdot6}[/tex]A=$4,431.31 ------> the totalFind out the interest
I=A-P
I=4,431.31-3,200
I=$1,231.31 -----> interestSimplify (3^z)^6 leave your answer in exponential notation
[tex](3^z)^6[/tex][tex]3^{6z}[/tex]
Find the measure of the numbered angles in the rhombus (m1, m2, and m3).
The diagonals of a rhombus intersect at right angles. So, the m<1 is 90 degrees.
The diagonals of a rhombus bisect each vertex angle.
Therefore, the angle of vertex of 24 degree angle angle is 24x2=48.
The opposite angle of 48 degree angle is also 48 degrees. Since the angle is bisected by diagonal,m<2=24 degree.
The sum of opposite angles, 48+48=96.
The sum of other two equal opposite angles, 360-96=264.
The half of 264 is one angle, So, 264/2=132. Again <3=132/2=66.
m<1=90, m<3=66, m<2=24
Which equation can be used to find the solution of (1/4)y+1=64 ? −y−1=3y−1=3−y+1=3y + 1 = 3
1/4 and 64 can be expressed as follows:
[tex]\begin{gathered} \frac{1}{4}=4^{-1} \\ 64=4^3 \end{gathered}[/tex]Substituting into the equation:
[tex]\begin{gathered} (4^{-1})^{y+1}=4^3 \\ 4^{(-1)(y+1)}=4^3 \\ 4^{-y-1}=4^3 \\ -y-1=3 \end{gathered}[/tex]Simplify and then evaluate the equation when x=4 and y =2
We need to plug in
x = 4
y = 2
into the expression and simplify/evaluate.
Let's evaluate:
[tex]\begin{gathered} 5x+2(9y-x)-y \\ x=4,y=2 \\ So, \\ 5(4)+2(9(2)-(4))-(2) \\ =20+2(18-4)-2 \\ =20+2(14)-2 \\ =20+28-2 \\ =46 \end{gathered}[/tex]Answer46Select the correct answer.Solve the equation using the method of completing the square.A. B. C. D.
Answer:
C. -4 ± 2√6
Explanation:
The given equation is
3x² + 24x - 24 = 0
First, add 24 to both sides
3x² + 24x - 24 + 24 = 0 + 24
3x² + 24x = 24
And factorize 3 on the left side
3(x² + 8x) = 24
Then, to complete the square, we need to add and substract (b/2)² to the expression in parenthesis. In this case, b = 8, so
(b/2)² = (8/2)² = 4² = 16
Then, add and subtract 16 as follows
3(x² + 8x + 16 - 16) = 24
3(x² + 8x + 16) - 3(16) = 24
3(x² + 8x + 16) - 48 = 24
Finally, we can factorize and solve for x
3(x + 4)² - 48 = 24
3(x + 4)² - 48 + 48 = 24 + 48
3(x + 4)² = 72
3(x + 4)²/3 = 72/3
(x + 4)² = 24
Solving for x, we get
[tex]\begin{gathered} x+4=\pm\sqrt{24} \\ x+4-4=-4\pm\sqrt{24} \\ x=-4\pm\sqrt{24} \\ x=-4\pm\sqrt{4\cdot6} \\ x=-4\pm2\sqrt{6} \end{gathered}[/tex]Therefore, the answer is
C. -4 ± 2√6
the sum of 1/3 and 3/8
Answer:
17/24
Explanation:
To add the fractions
[tex]\frac{1}{3}+\frac{3}{8}[/tex]we first find their common denominators.
The common multiple of 3 and 8 is 24 because 3 * 8 = 24; therefore,
[tex]\frac{1}{3}+\frac{3}{8}=\frac{1\cdot8}{3\cdot8}+\frac{3\cdot3}{8\cdot3}[/tex][tex]=\frac{8}{24}+\frac{9}{24}[/tex]Adding the numerators gives
[tex]\frac{8}{24}+\frac{9}{24}=\frac{17}{24}[/tex]Hence,
[tex]\frac{1}{3}+\frac{3}{8}=\frac{17}{24}[/tex]2. Write the equation of the graph shown below. 3 1 -2 0 2 1-
The function in the graph is V shaped, this indicates that it corresponds to a function of an absolute value of x:
[tex]f(x)=|x|[/tex]The V opens downwards, which means that the coefficient that multiplies the module (a) is negative:
[tex]f(x)=-|x|[/tex]→ This means rthat when we calculate the value of "a", this value has to be negative
As you can see in the graph, the vertex of the function is (0,3)
Following the vertex form:
[tex]f(x)=a|x-x_v|+y_v[/tex]Where xv represents the x-coordinate of the vertex and yv represents the y-coordinate of the vertex. Replace them in the formula and we get that:
[tex]\begin{gathered} f(x)=a|x-0|+3 \\ f(x)=a|x|+3 \end{gathered}[/tex]Now all we need to do is determine the value of "a", for this we have to use one point of the function and replace it in the formula, this way "a" will be the only unknown.
Lets take for example one of the roots (points where the function crosses the x-axis)
Point (1, 0)→ replace it in the formula
[tex]\begin{gathered} 0=a|1|+3 \\ 0=a+3 \\ a=-3 \end{gathered}[/tex]Now that we know the value of a, we can determine the wquation of the function as
[tex]f(x)=-3|x|+3[/tex]When a positive number x is divided by 7, the remainder is 4. What is
the remainder when x is divided by 4?
When a positive number x is divided by 7, the remainder is 4. The remainder when x is divided by 4 is 7.
What is a remainder?
The quantity "leftover" after executing a computation in mathematics is referred to as the remainder. The remainder is the integer that remains after dividing two integers to get an integer quotient in mathematics.
The remainder operator (%) returns the amount of one argument that is left over after dividing it by another operand. For instance, when 41 is divided by 7, the remaining is 6 and the quotient is 5.
Solution Explained:
A/Q
x / 7 = 4
Solving this equation
x = 4 X 7 = 28
Now putting the value of x in the equation
x / 4
= 28 / 4 = 7
Therefore, the remainder when x is divided by 4 is 7.
To learn more about remainder, use the link given
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line AB and CD intersect at E. if the measurement of angle AEC = 12x+5 and the measurement of angle DEB = x+49, find the measurement of angle DEB
We will start by drawing the lines and angles:
By the properties of the angles that are opposed by the vertex, we know that the measure of the angle AEC and the measure of the angle DEB are the same.
So we can express:
[tex]\begin{gathered} m\text{AEC}=m\text{DEB} \\ 12x+5=x+49 \\ 12x-x=49-5 \\ 11x=44 \\ x=\frac{44}{11} \\ x=4 \end{gathered}[/tex]So we can calculate DEB as:
[tex]\text{DEB}=x+49=4+49=53[/tex]The angle DEB has a measure of 53 degrees.
A shipment of 10 computers contains 4 with defects. Find the probability that a sample of size 4, drawn from the 10, will not contain a defective computer,The probability is:
ANSWER
[tex]P=\frac{81}{625}[/tex]EXPLANATION
There are 4 defects out of 10 total computers. This means that there are 6 computers without defects.
The probability that 1 computer selected will not be defective is the total number of non-defective computers divided by the total number of computers:
[tex]P(one-without-defect)=\frac{6}{10}[/tex]Therefore, if a sample of 4 computers is selected, the probability that the sample will not contain a defective computer is:
[tex]\begin{gathered} P=\frac{6}{10}\cdot\frac{6}{10}\cdot\frac{6}{10}\cdot\frac{6}{10}=(\frac{6}{10})^4 \\ P=\frac{81}{625} \end{gathered}[/tex]Can someone please help me do #6 and #8 please
#6:
As it's a rhombus, the diagonal is a bisector, so:
med 2 = 27
med 3 = 27
and
med 5 = 27
med 4 = med 1
Also, the sum of interior angles of a triangle is 180 degrees. Then:
27 + 27 + med 1 = 180
med 1 = 126
med 4 = 126
_+_=10.5 _-3.25=_help me pls
These questions can have multiple answers
for instance,
a)
_+_=10.5
8.5 + 2 = 10.5
5.5 + 5 = 10.5
3.5 +7 = 10.5
5.25 + 5.25 = 10.5
b)
_-3.25 =_
7 - 3.25 = 3.75
7.25 - 3.25 = 4
10. 5 - 3.25 = 7.25
c)
if each _ have the same value
x + x = 10.5
2x= 10.5
x= 5.25
d)
if each _ have the same value
_-3.25 =_
x -3.25= x
x-x = 3.25
0= 3.25
In this case, each x cannot be the same, it would have to be a number that you subtract 3. 25 and it remains the same number. That is not possible.
but if i use x= 5.25
5.25- 3.25= 2
=Volume of a cylinderThe diameter of a cylindrical construction pipe is 6 ft. If the pipe is 25 ft long, what is its volume?Use the value 3.14 for it, and round your answer to the nearest whole number.Be sure to include the correct unit in your answer.
The volume of a cylinder is given by the following formula:
[tex]V=\frac{\pi\cdot h\cdot d^2}{4}[/tex]Where h is the height and d is the diameter.
We can consider the length of the pipe as the height of the cylinder.
Then h=25 ft and d=6 ft. Replace these values in the formula and solve for V:
[tex]\begin{gathered} V=\frac{3.14\cdot25ft\cdot(6ft)^2}{4} \\ V=\frac{3.14\cdot25ft\cdot36ft^2}{4} \\ V=\frac{2826ft^3}{4} \\ V=706.5ft^3 \\ V\approx707ft^3 \end{gathered}[/tex]The volume is 707 ft^3
Ben earned $400 dollars last month.He worked 3 days in the first week andalso worked 2 days in the secondweek. How much does he earn eachday?
Given Data:
Ben earned $400 last month.
Since in the academic calendar the last month was July consisting of 31 days.
Therefore the amount earned per day can be calculated as
[tex]\frac{400}{31}[/tex]Now, He worked 3 days in the first week and 2 days in the second week.
So the total number of working days is 5.
Therefore the amount earned for 5 days will be
[tex]\frac{400}{31}\times5=64.51[/tex]Therefore the amount for 6 days is approximate $65.
And Hence for each day it is $13.
what is the value of x and y ?2x+3=Y
There can be infinite solutions for x and y, this is because if we look at the equation like a slope intercept equation
[tex]\begin{gathered} 2x+3=y \\ y=2x+3 \end{gathered}[/tex]we can see that this is the equation for a straight line.
if we graph it
All values of x and y that are obtain by the line can be a solution to the equation given.
Factor. x2 − x − 72 (x − 8)(x + 9) (x − 6)(x + 12) (x + 8)(x − 9) (x + 6)(x − 12)
The solution of the given equation are; (x + 8)(x − 9)
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We have been given the quadratic equation as;
x² − x − 72
Solving;
x² − (9-8)x − 72
x² − 9x +8x− 72
The factors are;
(x + 8)(x − 9)
Therefore, the solution of the given equation are; (x + 8)(x − 9)
Learn more about quadratic equations;
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Given: AB - BC, ZA ZC and BD bisects ABC. Prove: A ABD ~ ACBD.
Since BD bisects ABC, then angles ADB and BDC are congruent. Now that we have that both triangles ABD and CBD have the same two sides and angle, we have that they are congruent (because the side-angle-side postulate)
Find the sales tax in total cost of espresso machine that cost $46.95 the tax rate is 4% rounding your answer to the nearest cent
Given:
The total cost of espresso machine costs $46.95. and the tax rate is 4%.
To find:
Find the sales tax?
Explanation:
[tex]Sale\text{s tax=Sales tax percenatge}\times pre-tax\text{ cost}[/tex][tex]Total\text{ cost=Pre-tax value +Sales tax}[/tex]Solution:
We will start by converting sales tax percentage into a decimal by moving
the point two spaces to the left.
6%=0.06
Now, we need to multiply the pre-max cost of this item by this value
in order to calculate the sales tax cost
[tex]\begin{gathered} Sales\text{ tax=}0.04\times46.95 \\ Sales\text{ tax=1.878} \end{gathered}[/tex]Round to two decimal places
[tex]Sales\text{ tax=\$1.88}[/tex]Last, add this value of the pre-tax value of the item to find the total cost.
[tex]\begin{gathered} Total\text{ cost=Pre tax value + Sales tax} \\ Total\text{ Cost=46.95+1.88} \\ Total\text{ cost=}48.83 \end{gathered}[/tex]Hence, these are the required values.
Solve the equation, give the exact solution then approximate the solution to the nearest hundredth
Given the expression:
[tex]10-3x^2=4[/tex]We can find its solution by solving like a linear equation up until the exponent:
[tex]\begin{gathered} 10-3x^2=4 \\ \Rightarrow-3x^2=4-10 \\ \Rightarrow-3x^2=-6 \\ \Rightarrow x^2=\frac{-6}{-3}=2 \\ x^2=2 \end{gathered}[/tex]now, we can apply the square root on both sides to get the following:
[tex]\begin{gathered} \sqrt[]{x^2}=\sqrt[]{2} \\ \Rightarrow x=\pm\sqrt[]{2=} \\ x=\pm1.41 \end{gathered}[/tex]therefore, the solutions of the equation are x=1.41 and x=-1.41
Once Farid spends 15 minutes on a single level in his favorite video game, he loses a life. Hehas already spent 10 minutes on the level he's playing now.Let x represent how many more minutes Farid can play on that level without losing a life.Which inequality describes the problem?
If he spends 15 minutes on a single level, he loses his life.
He has already spent 10 minutes on the level he is playing now.
x = the number of minutes he can play without losing a life.
The inequalities that can be use to represent this scenario will be
[tex]10+x<15[/tex]Help me please don’t use me for pointsthis answer well be 12×
Answer:
9x + 3
Explanation:
Given the below expression;
[tex]1x-7+8x+10[/tex]The 1st to solving the above is to group like terms;
[tex]1x+8x-7+10[/tex]Let's go ahead and evaluate;
[tex]9x+3[/tex]Use a proportion to find the missing side length, x.
Answer:
The measure of angle ABC is;
[tex]m\measuredangle ABC=72^0[/tex]Explanation:
Given the triangle ABC.
Recall that the sum of angles in a triangle is 180 degrees;
[tex]8x+6x+6x=180[/tex]solving for x, we have;
[tex]\begin{gathered} 8x+6x+6x=180 \\ 20x=180 \\ x=\frac{180}{20} \\ x=9 \end{gathered}[/tex]From the diagram,
[tex]\begin{gathered} \measuredangle ABC=8x \\ \measuredangle ABC=8(9) \\ \measuredangle ABC=72^0 \end{gathered}[/tex]Therefore, the measure of angle ABC is;
[tex]m\measuredangle ABC=72^0[/tex]need help converting point slope form equation to slope intercept form(y+10)=1/3(x+9)
The slope-intercept form is
→ y = m x + b
→ m is the slope
→ b is the y-intercept
∵ The given equation is
[tex]y+10=\frac{1}{3}(x+9)[/tex]First, multiply the bracket (x + 9) by 1/3
[tex]\begin{gathered} \because y+10=\frac{1}{3}(x)+\frac{1}{3}(9) \\ \therefore y+10=\frac{1}{3}x+3 \end{gathered}[/tex]Subtract 10 from both sides
[tex]\begin{gathered} \because y+10-10=\frac{1}{3}x+3-10 \\ \therefore y+0=\frac{1}{3}x-7 \\ \therefore y=\frac{1}{3}x-7 \end{gathered}[/tex]The equation in the slope-intercept form is y = 1/3 x - 7
With cell phones being so common these days, the phone companies are all competing to earn business by offering various calling plans. One of them, Horizon, offers 700 minutes of calls per month for $45.99, and additional minutes are charged at 6 cents per minute. Another company, Stingular, offers 700 minutes for $29.99 per month, and additional minutes are 35 cents each. For how many total minutes of calls per month is Horizon’s plan a better deal?
For the Horizon offer
There is a cost of $45.99 for 700 minutes plus 6 cents for each additional minute
Since 1 dollar = 100 cents, then
6 cents = 6/100 = $0.06
If the total number of minutes is x, then
The total cost will be
[tex]C_H=45.99+(x-700)0.06\rightarrow(1)[/tex]For the Stingular offer
There is a cost of $29.99 for 700 minutes plus 35 cents for each additional minute
35 cents = 35/100 = $0.35
For the same number of minutes x
The total cost will be
[tex]C_S=29.99+(x-700)0.35\rightarrow(2)[/tex]For Horizon to be better that means, it cost less than the cost of Stingular
[tex]\begin{gathered} C_HSubstitute the expressions and solve for x[tex]\begin{gathered} 45.99+(x-700)0.06<29.99+(x-700)0.35 \\ 45.99+0.06x-42<29.99+0.35x-245 \\ (45.99-42)+0.06x<(29.99-245)+0.35x \\ 3.99+0.06x<-215.01+0.35x \end{gathered}[/tex]Add 215.01 to both sides
[tex]\begin{gathered} 3.99+215.01+0.06x<-215.01+215.01+0.35x \\ 219+0.06x<0.35x \end{gathered}[/tex]Subtract 0.06x from both sides
[tex]\begin{gathered} 219+0.06x-0.06x<0.35x-0.06x \\ 219<0.29x \end{gathered}[/tex]Divide both sides by 0.29 to find x
[tex]\begin{gathered} \frac{219}{0.29}<\frac{0.29x}{0.29} \\ 755.17Then x must be greater than 755.17The first whole number greater than 755.17 is 756
The total minutes should be 756 minutes per month for Horizon's to be the better deal.
The sum of sixteen times a number and twelve is 172. Find the number.
Answer:
Step-by-step explanation:
1. (16 · x) + 12 = 172
2. x= 172-12/16
3. x = 10
4. The number is 10.
The circle at the right represents a planet. The radius of the planet is about 6600 km. Find the distance to the inizon that a person can seeon a clear day from the following heighth above the planeth 7 km
Which answer choice represents a simplified form of the expression 2.5 + 7 1 - 2.3 - 4?* O (2.5 + 2.3) - 7-4 0 (2.5 - 2.3) - (7-4) O (2.5 - 2.3) + (7 - 4) 4 + 7 + (2.5 - 2.3)