The table shows the earnings and the number of hours worked for five employees. complete the table by finding the missing values.
Answers
The first employee
[tex]\begin{gathered} He\text{ earns a total of \$12.75} \\ \text{His working rate is \$}8.50\text{ per hour} \\ \text{Hours he workd can be calculated below} \\ \text{ \$8.50 = 1 hour} \\ \text{ \$12.75 =?} \\ \text{ number of hours=}\frac{12.75}{8.50} \\ \text{ number of hours = 1.5 hours} \end{gathered}[/tex]The second employee
[tex]\text{ earning per hour = }\frac{19.09}{2.3}=\text{ \$8.3 per hour}[/tex]The third employee
[tex]\begin{gathered} \text{ \$7.75=1 hour} \\ \text{ \$26.}35=\text{?} \\ \text{ number of hours=}\frac{26.35}{7.75}=3.4\text{ hours} \end{gathered}[/tex]The fourth employee
[tex]\text{earning per hour = }\frac{49.50}{4.5}=\text{ \$}11\text{ per hour}[/tex]The fifth employee
[tex]\text{earning per hour=}\frac{31.50}{1.5}=\text{ \$21 per hour}[/tex]Related Questions
HELP PLEASE!
Dave has a piggy bank which consists of dimes, nickels, and pennies. Dave has seven
more dimes than nickels and ten more pennies than nickels. If Dave has $3.52 in his piggy bank, how many of each coin does he have?
Answers
Dave has 17 nickels, 24 dimes and 27 pennies in his piggy bank.
According to the question,
We have the following information:
Dave has 7 more dimes than nickels and 10 more pennies than nickels.
Now, let's take the number of nickels to be x.
So,
Dimes = (x+7)
Pennies = (x+10)
Now, Dave has $3.52 in his piggy bank.
We will convert nickels, dimes and pennies into dollars.
We know that 1 nickel = 0.05 dollars, 1 dime = 0.1 dollars and 1 pennies = 0.01 dollars.
Now, we will convert the given numbers of nickel, dime and pennies into dollars.
x Nickels in dollars = $0.05x
(x+7) dimes in dollars = $0.1(x+7)
(x+10) pennies in dollars = $0.01(x+10)
Now, we will them.
0.05x + 0.1(x+7) + 0.01(x+10) = 3.52
0.05x + 0.1x + 0.7 + 0.01x + 0.1 = 3.52
0.16x + 0.8 = 3.52
0.16x = 3.52-0.8
0.16x = 2.72
x = 2.72/0.16
x = 17
Now, we have:
Number of nickels = 17
Number of dimes = (17+7)
Number of dimes = 24
Number of pennies = (17+10)
Number of pennies = 27
Hence, the number of nickels, dimes and pennies are 17, 24 and 27 respectively.
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Determine the angle relationship. Drag the correct answer to the blank. what is the angle relationship of < 3 & <7
Answers
we have that
between m<3 and m<7 -----> no relationship (because q and p are not parallel)
Part 2
the relationship between m<12 and m<10
is
vertical angles
m<12=m<10 ------> by vertical angles
What is the measure of the base of the rectangle if the area of the triangle is 32 ft2 ?A) 8 ftB) 16 ft C) 32 ftD) 64 ft
Answers
Answer:
B) 16 ft
Explanation:
The area of a triangle is equal to
[tex]Area\text{ =}\frac{Base\times Height}{2}[/tex]We know that the area is 32 ft² and the height is 4 ft, so replacing these values, we get
[tex]32=\frac{\text{Base}\times4}{2}[/tex]Now, we can solve for the base. So multiply both sides by 2
[tex]\begin{gathered} 32\times2=\frac{\text{Base }\times4}{2}\times2 \\ 64=\text{Base }\times4 \end{gathered}[/tex]Then divide both sides by 4
[tex]\begin{gathered} \frac{64}{4}=\frac{Base\times4}{4} \\ 16=\text{Base} \end{gathered}[/tex]Therefore, the measure of the base is 16 ft
Please help i need the answers for a test and how to work em out for the future
Answers
Given: The angles as shown in the image
[tex]\begin{gathered} m\angle DEY=105^0 \\ m\angle DEF=27x+3 \\ m\angle YEF=6x+3 \end{gathered}[/tex]To Determine: The measure of angle DEF
Solution
It can be observed that
[tex]\begin{gathered} m\angle DEY+m\angle YEF=m\angle DEF \\ Therefore \end{gathered}[/tex][tex]\begin{gathered} 105^0+6x+3=27x+3 \\ 105=27x-6x+3-3 \\ 105=21x \\ x=\frac{105}{21} \\ x=5 \end{gathered}[/tex][tex]\begin{gathered} m\angle DEF=21x+3 \\ =21(5)+3 \\ =105+3 \\ =108 \end{gathered}[/tex]Question 12
Given:
[tex]\begin{gathered} m\angle UIJ=x+43 \\ m\angle HIJ=66 \\ m\angle HIU=x+37 \end{gathered}[/tex]To Determine: The measure of angle HIU
Solution:
It can be observed that
[tex]m\angle UIJ+m\angle HIU=m\angle HIJ[/tex][tex]\begin{gathered} x+43+x+37=66^0 \\ Collect-like-terms \\ x+x+43^0+37^0=66^0 \\ 2x+80^0=66^0 \\ 2x=66^0-80^0 \\ 2x=-14^0 \\ x=-\frac{14^0}{2} \\ x=-7^0 \end{gathered}[/tex]Therefore, the measure of angle HIU would be
[tex]\begin{gathered} m\angle HIU=x+37^0 \\ m\angle HIU=-7+37^0 \\ m\angle HIU=30^0 \end{gathered}[/tex]Hence, the measure of angle HIU is 30⁰
Find the 5th term of the arithmetic sequence -5x – 5, -123 – 8,- 19x – 11, ...Answer:Submit Answer
Answers
5x – 5, -123x – 8,
- 19x – 11, ...
Difference is =
Find decimal notation for 100%
Answers
The decimal notation of percentage is the quotient of the percentage divided by 100.
So it follows that :
[tex]\frac{100\%}{100}=1[/tex]The answer is 1
Which 3 pairs of side lengths are possible measurements for the triangle?
Answers
SOLUTION
From the right triangle with two interior angles of 45 degrees, the two legs are equal in length, that is AB = BC
And from Pythagoras, the square of the hypotenuse (AC) is equal to the square of the other two legs or sides (AB and AC)
So this means
[tex]\begin{gathered} |AC|^2=|AB|^2+|BC|^2 \\ since\text{ AB = BC} \\ |AC|^2=2|AB|^2,\text{ also } \\ |AC|^2=2|BC|^2 \end{gathered}[/tex]So from the first option
[tex]\begin{gathered} BC=10,AC=10\sqrt{2} \\ |AC|^2=(10\sqrt{2})^2=100\times2=200 \\ 2|BC|^2=2\times10^2=2\times100=200 \end{gathered}[/tex]Hence the 1st option is correct, so its possible
The second option
[tex]\begin{gathered} AB=9,AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times9^2=2\times81=162 \\ 324\ne162 \end{gathered}[/tex]Hence the 2nd option is wrong, hence not possible
The 3rd option
[tex]\begin{gathered} BC=10\sqrt{3},AC=20 \\ |AC|^2=20^2=400 \\ 2|BC|^2=2\times(10\sqrt{3})^2=2\times100\times3=600 \\ 400\ne600 \end{gathered}[/tex]Hence the 3rd option is wrong, not possible
The 4th option
[tex]\begin{gathered} AB=9\sqrt{2},AC=18 \\ |AC|^2=18^2=324 \\ 2|AB|^2=2\times(9\sqrt{2})^2=2\times81\times2=324 \\ 324=324 \end{gathered}[/tex]Hence the 4th option is correct, it is possible
The 5th option
AB = BC
This is correct, and its possible
The last option
[tex]\begin{gathered} AB=7,BC=7\sqrt{3} \\ 7\ne7\sqrt{3} \end{gathered}[/tex]This is wrong and not possible because AB should be equal to BC
Hence the correct options are the options bolded, which are
1st, 4th and 5th
I need a math tutor asap .
Answers
For this exercise you need to remember that a Cube is a solid whose volume can be calculated using the following formula:
[tex]V=s^3[/tex]Where "V" is the volume of the cube and "s" is the length of any edge of the cube (because all the edges of a cube have the same length).
For example, if you have a cube and you know that:
[tex]s=5\operatorname{cm}[/tex]You can substitute this value into the formula and then evaluate, in order to find the volume of the cube. This would be:
[tex]\begin{gathered} V=(5\operatorname{cm})^3 \\ V=125\operatorname{cm}^3 \end{gathered}[/tex]The answer is:
You can find it using the formula
[tex]V=s^3[/tex]Where "s" is the length of any edge of the cube
Given two functions f(x) and g(x):f(x) = 8x - 5,8(x) = 2x2 + 8Step 1 of 2 Form the composition f(g(x)).Answer 2 PointsKeypadKeyboard Shortcutsf(g(x)) =>Next
Answers
we have the functions
[tex]\begin{gathered} f(x)=8x-5 \\ g(x)=2x^2+8 \end{gathered}[/tex]Find out f(g(x))
Substitute the variable x in the function f(x) by the function g(x)
so
[tex]\begin{gathered} f\mleft(g\mleft(x\mright)\mright)=8(2x^2+8)-5 \\ f(g(x))=16x^2+64-5 \\ f(g(x))=16x^2+59 \end{gathered}[/tex]The graph of function f is shown. The graph of an exponential function passes through (minus 0.25, 10), (0, 6), (5, minus 2) also intercepts the x-axis at 1 unit. Function g is represented by the table. x -1 0 1 2 3 g(x) 15 3 0 - 3 4 - 15 16 Which statement correctly compares the two functions? A. They have the same y-intercept and the same end behavior as x approaches ∞. B. They have the same x-intercept but different end behavior as x approaches ∞. C. They have the same x- and y-intercepts. D. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
Answers
The given data points from the graph of the exponential function, f, and the, values from the table of the function g, gives the statement that correctly compares the two functions as the option;
B. They have the same x–intercept but different end behaviours as x approaches ∞What is the end behaviour of a graph?The end behaviour of a function is the description of how the function behaves towards the boundaries of the x–axis.
The given points on the exponential function, f, are;
(-0.25, 10), (0, 6), (5, -2) and also the x–intercept (1, 0)
The points on the function g, obtained from the table of the values for g(x), expressed as ordered pairs are;
(-1, 15), (0, 3), (1, 0), (2, -34), (3, -16)
The coordinates of the x–intercept is given by the point where the y–value is zero.
The x–intercept for the exponential function, f, is therefore (1, 0)
Similarly, the x–intercept for the function, g, is (1, 0)
Therefore, both functions have the same x–intercept
However, the end behaviour of the function, f, as the x approaches infinity is that f(x) approaches negative infinity, while the end behaviour of the function, g, as the the value of x approaches infinity is g(x) is increasing towards positive infinity.
The correct option is therefore;
B. They have the same x–intercept but different end behaviour as x approaches ∞Learn more about the end behaviour of a function here:
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An equation that can be used to determine the total
Answers
The equation that we have to build has the following form:
[tex]y=mx+b[/tex]• The fixed cost of the phone is $88, which will be represented by ,b,.
,• The variable cost per month is $116.43, which will be represented by ,m,.
,• y ,is the dependent variable that we want to know (, C(t) ,)
,• x ,is the independent variable, in our case, ,t,.
Replacing the values given in the problem we get:
[tex]C(t)=116.93t+88[/tex]The cost for 22 months will be:
[tex]C(22)=116.93\cdot22+88[/tex][tex]C(22)=2660.46[/tex]Answer:
• Equation
[tex]C(t)=116.93t+88[/tex]• Cost in 22 months: $2660.46
Find an equation of the line. Write the equation using function notation.
Through (4, -1); perpendicular to 4y=x-8
The equation of the line is f(x) =
Answers
The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:
[tex]y = -4x+15[/tex].
What is a equation of line?These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
Given equation of line is:
4y=x-8
We have to convert the given line in slope-intercept form to find the slope of the line
Dividing both sides by 4.
[tex]y = \frac{1}{4}x-2[/tex]
Let [tex]m_{1}[/tex] be the slope of given line
Then,
[tex]m_{1}[/tex] = [tex]\frac{1}{4}[/tex]
Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line
As we know that product of slopes of two perpendicular lines is -1.
[tex]m_{1}*m_{2} = -1\\\frac{1}{4}*m_{2}=-1\\ m_{2} = -4[/tex]
The slope intercept form of line is given by
[tex]y = m_{2}x+c[/tex]
[tex]y = -4x+c[/tex]
to find the value of c, putting (4,-1) in equation
[tex]-1 = -4*4+c\\-1+16 = c\\c = 15[/tex]
Putting the value of c in the equation
[tex]y=-4x+15[/tex]
Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is [tex]y = -4x+15[/tex].
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what is the slope for the following points?(-1,1) and(3,3)
Answers
To find the slope for a line that connects the given points, use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are the given points.
Use:
(x1,y1) = (-1,1)
(x2,y2) = (3,3)
replace the values of the previous parameters in the formula for m:
[tex]m\text{ = }\frac{3-1}{3-(-1)}=\frac{2}{3+1}=\frac{2}{4}=\frac{1}{2}[/tex]Hence, the slope is 1/2
A projectile is fired vertically upwards and can be modeled by the function h(t)= -16t to the second power+600t +225 during what time interval will the project I’ll be more than 4000 feet above the ground round your answer to the nearest hundredth
Answers
Given:
[tex]h(t)=-16t^2+600t+225[/tex]To find the time interval when the height is about more than 4000 feet:
Let us substitute,
[tex]\begin{gathered} h(t)\ge4000 \\ -16t^2+600t+225\ge4000 \\ -16t^2+600t+225-4000\ge0 \\ -16t^2+600t-3775\ge0 \end{gathered}[/tex]Using the quadratic formula,
Here, a= -16, b=600, and c= -3775
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-600\pm\sqrt[]{600^2-4(-16)(-3775)}}{2(-16)} \\ =\frac{-600\pm\sqrt[]{360000^{}-241600}}{-32} \\ =\frac{-600\pm\sqrt[]{118400}}{-32} \\ =\frac{-600\pm40\sqrt[]{74}}{-32} \\ =\frac{-75\pm5\sqrt[]{74}}{-4} \\ t=\frac{-75+5\sqrt[]{74}}{-4},x=\frac{-75-5\sqrt[]{74}}{-4} \\ t=7.99709,t=29.5029 \end{gathered}[/tex]So, the interval is,
[tex]8.00\le\: t\le\: 29.50[/tex]A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the height, to the nearest foot, at a time of 3.8 seconds.
Answers
Given
The data can be modeled using a quadratic regression equation.
Using the general form of a quadratic equation:
[tex]y=ax^2\text{ + bx + c}[/tex]We should use a regression calculator to obtain the required coefficients. The graph of the equation is shown below:
The coefficients of the equation is:
[tex]\begin{gathered} a\text{ = -17.5 (nearest tenth)} \\ b\text{ = }249.0\text{ (nearest tenth)} \\ c\text{ = }-0.5 \end{gathered}[/tex]Hence, the regression equation is:
[tex]y=-17.5x^2\text{ + 249.0x -0.5}[/tex]We can find the height (y) at a time of 3.8 seconds by substitution:
[tex]\begin{gathered} y=-17.5(3.8)^2\text{ + 249}(3.8)\text{ - 0.5} \\ =\text{ }693 \end{gathered}[/tex]Hence, the height at time 3.8 seconds is 693 ft
Are the graphs of the equations parallel, perpendicular, or neither?x -3y = 6 and x - 3y = 9
Answers
The equation of a line in Slope-Intercept form, is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
By definition:
- The slopes of parallel lines are equal and the y-intercepts are different.
- The slopes of perpendicular lines are opposite reciprocals.
For this case you need to rewrite the equations given in the exercise in Slope-Intercept form by solving for "y".
- Line #1:
[tex]\begin{gathered} x-3y=6 \\ -3y=-x+6 \\ y=\frac{-x}{-3}+(\frac{6}{-3}) \\ \\ y=\frac{x}{3}-2 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} m_1=\frac{1}{3} \\ \\ b_1=-2 \end{gathered}[/tex]- Line #2:
[tex]\begin{gathered} x-3y=9 \\ -3y=-x+9 \\ y=\frac{-x}{-3}+(\frac{9}{-3}) \\ \\ y=\frac{x}{3}-3 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} m_2=\frac{1}{3} \\ \\ b_2=-3_{}_{} \end{gathered}[/tex]Therefore, since:
[tex]\begin{gathered} m_1=m_2 \\ b_1\ne b_2 \end{gathered}[/tex]You can conclude that: The graphs of the equation are parallel.
3 * 10 ^ - 6 = 4.86 * 10 ^ - 4 in scientific way
Answers
Answer:
3*10=30
10^-6=1^-6. (10 raised to the power of-6)
therefore 3*1^-6=3
is equal to
4.86*10=48.6
10^-4=1^-4
therefore 48.6*1^-4=48.6
Alexa claims that the product of 2.3 and 10^2 is 0.23. Do you agree or disagree? Explain why or why not?
Answers
Answer:
disagree
Step-by-step explanation:
product = 2.3 * 10²
= 2.3 * 100
= 230
thus, the answer is different from the one acclaimed by Alexa.
Find the future value using the future value formula and a calculator in order to achieve $420,000 in 30 years at 6% interest compounded monthly
Answers
The present value of in order to achieve $420000 in 30 years at 6% interest compounded monthly is $69737.60
The future value = $420000
The time period = 30 years
The interest percentage = 6%
The interest is compounded monthly
A = [tex]P(1+\frac{i}{f})^{fn}[/tex]
Where A is the final value
P is principal amount
i is the interest rate
f frequency where compound interest is added
n is the time period
Substitute the values in the equation
420000 = P × [tex](1+\frac{0.06}{12} )^{(12)(30)[/tex]
420000 = P × 6.02
P = 420000 / 6.02
P = $69737.60
Hence, the present value of in order to achieve $420000 in 30 years at 6% interest compounded monthly is $69737.60
The complete question is:
Find the present value using the future value formula in order to achieve $420,000 in 30 years at 6% interest compounded monthly
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there are approximately 1.2 x 10^8 households in the U.S. If the average household uses 400 gallons of water each day what is the total number of gallons of water used by households in the US each day ? Please Answer this im scientific notation
Answers
According to the given data we have the following:
total households in the US=1.2*10^8. hence:
[tex]1.2*10^8=120000000[/tex]average household uses 400 gallons of water each day
let x=total number of gallons of water used by households in the US each day
Therefore x=total households in the US*average gallons of water households uses each day
x=120,000,000*400
x=48,000,000,000
The total number of gallons of water used by households in the US each day is 48,000,000,000
Which values are solutions to the inequality below? Check all that applySqrt x>=9Choices are:-2, 82, 32, 180, 99, 63
Answers
We notice the following:
[tex]\begin{gathered} \sqrt[]{x}\ge9\ge0 \\ \Rightarrow \\ x\ge81 \end{gathered}[/tex]Then, possible solutions of the inequality are all real numbers greater or equal than 81. From the given set of solution, those numbers that fullfill that requirement are:
[tex]82,\text{ 180 and 99}[/tex]Find x.special 10A. 3B. 23√3- this is in fractionC. 6√3D. 3√3
Answers
First, we need to remember the cosine formula which is: cosine(theta)= adjacent/hypotenuse, now let's apply the formula to the triangle we have:
By using the formula we find that x=3√3 .
The answer is D.
Plot Points & Graph Function (Table Given)
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We have the next function
[tex]y=-\sqrt[]{x}+3[/tex]We need to calculate some points
x y
0 3
1 2
4 1
9 0
Let's plot the points and then we connect them in order to obtain the graph
1. The equations y = x2 + 6x + 8 and y = (x + 2)(x+4) both define thesame quadratic function.Without graphing, identify the x-intercepts and y-intercept of the graph.Explain how you know
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Given the quadratic equation
[tex]y=x^2\text{ +6x + 8}[/tex](1) x-intercepts are -2 and -4 is the points that pass through the x-axis
when y = 0
[tex]\begin{gathered} y\text{ = 0 } \\ x^2\text{ + 6x + 8 = 0} \\ x^2+2x\text{ +4x +8 = 0} \\ (x\text{ + 2)(x +4)=0} \\ x\text{ +2 = 0 or x +4 =0} \\ x\text{ = -2 or x = -4} \end{gathered}[/tex](11) y-intercepts = 8 is the points that pass through the y axis when x = 0
[tex]\begin{gathered} y=x^2\text{ +6x +8} \\ \text{when x = 0} \\ y=0^2\text{ +6(0) +8} \\ \text{y = 8} \end{gathered}[/tex]
Can someone help out with a math prob?
pic of question below
Answers
The polar equation of the curve with the given Cartesian equation is r = √7
How to convert polar equation to cartesian equationGiven the Cartesian equation: x² + y² = 7
The relationships between polar and cartesian equation :
x = r cosθ
y = r sinθ
Where r is the radius and θ is the angle
Put the values of x and y into the given cartesian equation:
(r cosθ)² + (r sinθ)² = 7
r²cos²θ + r²sin²θ = 7
r²(cos²θ + sin²θ) = 7
Since the trigonometric identity cos²θ + sin²θ = 1
r²(1) = 7
r² = 7
r = √7
Therefore, the polar equation for the represented curve is r = √7
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In the scoring for a game, points can be negative and positive. There were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times. How many more times would 5.5 points need to be scored to have a total gain greater than 15 points?
A. 1
C. 3
B. 2
D. 4
Answers
The number of times that 5.5 points is need to be scored to have a total gain greater than 15 points is A. 1
How to calculate the value?From the information, it was stated that there were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times.
In this case, the entire score will be:
= (-3.25 × 4) + (-2.75 × 5) + (3 × 2) + (5.5 ×4)
= -13 - 13.75 + 6 + 22
= 11.25
Therefore, the times that 5.5 points is needed to be scored to have a total gain greater than 15 will be 1 time since 11.25 + 5.5 = 16.75. This is more than 15.
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Find the area and the perimeter of the following rhombus. round to the nearest whole number if needed.
Answers
ANSWER
[tex]\begin{gathered} A=572 \\ P=96 \end{gathered}[/tex]EXPLANATION
To find the area of the rhombus, we have to first find the length of the other diagonal.
We are given half one diagonal and the side length.
They form a right angle triangle with half the other diagonal. That is:
We can find x using Pythagoras theorem:
[tex]\begin{gathered} 24^2=x^2+16^2 \\ x^2=24^2-16^2=576-256 \\ x^2=320 \\ x=\sqrt[]{320} \\ x=17.89 \end{gathered}[/tex]This means that the length of the two diagonals is:
[tex]\begin{gathered} \Rightarrow2\cdot16=32 \\ \Rightarrow2\cdot17.89=35.78 \end{gathered}[/tex]The area of a rhombus is given as:
[tex]A=\frac{p\cdot q}{2}[/tex]where p and q are the lengths of the diagonal.
Therefore, the area of the rhombus is:
[tex]\begin{gathered} A=\frac{32\cdot35.78}{2} \\ A=572.48\approx572 \end{gathered}[/tex]The perimeter of a rhombus is given as:
[tex]P=4L[/tex]where L = length of side of the rhombus
Therefore, the perimeter of the rhombus is:
[tex]\begin{gathered} P=4\cdot24 \\ P=96 \end{gathered}[/tex]The product two consequences positive even numbers is 728. Find the smaller of the two numbers. The smaller number is
Answers
Let the first number = n
So second number = n+2
the product of number is 728.
That mean:
[tex]n(n+2)=728[/tex]Solve the equation:
[tex]\begin{gathered} n(n+2)=728 \\ n^2+2n=728 \\ n^2+2n-728=0 \end{gathered}[/tex][tex]\begin{gathered} n^2+2n-728=0 \\ n^2+28n-26n-728=0 \\ n(n+28)-26(n+28)=0 \\ (n+28)(n-26)=0 \\ n=-28;n=26 \end{gathered}[/tex]For positive number is n=26.
scond number is:
[tex]\begin{gathered} =n+2 \\ =26+2 \\ =28 \end{gathered}[/tex]So smaller number is 26.
C) 1) if Z1 and 22 are complementary angles, and mZ1 = 74°; find m22.
Answers
Answer:
16
Explanation:
The angles ∠1 and ∠2 are complementary, meaning
[tex]\angle1+\angle2=90^o[/tex]Visually,
Now, ∠1 = 74; therefore,
[tex]74^o+\angle2=90^o[/tex]subtracting 74 from both sides gives
[tex]\angle2=90^o-74^o[/tex][tex]\angle2=16^o[/tex]which is our answer!
Transformations that preserve shape and size are called rigid motions. Find a definition of just the word rigid using the internet and write it below.
Answers
Simply put,
Rigid means not moving.
In transformations, rigid motions are transformations that preserve distance.