Solution
Step 1
Obey the multiplication law of indices where
[tex]a^b\times a^{d\text{ }}=a^{b+d}[/tex]So that we will have
[tex]5\times3\times10^{13}\times10^{15}[/tex][tex]\begin{gathered} 15\times10^{13+15} \\ =15\times10^{28} \end{gathered}[/tex]42.1069 rounded to the nearest thousandth is
ANSWER
42.107
EXPLANATION
To round a number to the nearest thousandth we have to look at the next number. If that number is 5 or greater than 5, then we have to add 1 to the thousandths. If it's less than 5, then we leave it like it is and eliminate the other decimals.
In this case, the next number to the thousandth is 9, which is greater than 5. Therefore, we have to turn the 6 into a 7: 42.107
b. Shirley was given the following points and asked to calculate the area, but her graph paper is not big enough. Calculate the area of Shirley's rectangle, and explain to her how she can determine the area without graphing the points. Shirley's points (352, 150), (352, 175), (456, 150), and (456, 175)
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]Create a real-world problem involving a cube - Use a perfect cube as its volume - Show using cube roots to find one edge
PART A
A box of sugar has equal lengths of 6 inches. Calculate the volume of sugar that can fill the box.
The volume of the box can be calculated using the cubic volume formula given to be:
[tex]V=l^3[/tex]Therefore, the volume of the box of sugar is calculated to be:
[tex]\begin{gathered} V=6^3 \\ V=216\text{ cubic inches} \end{gathered}[/tex]PART B
An ice cube is said to contain a volume of 8 cubic inches of water. What will be the length of one side of the cube?
The length of the cube can be calculated using the formula:
[tex]l=\sqrt[3]{V}[/tex]Hence, we can solve to be:
[tex]\begin{gathered} l=\sqrt[3]{8} \\ l=2\text{ inches} \end{gathered}[/tex]Find the value of angle B, rounding to the nearest tenth of a degree.
Law of Cosines.
- For a triangle ABC with sides labeled a,b, and c:
[tex]a^2=b^2+c^2-2bc\cos A[/tex][tex]b^2=a^2+c^2-2ac\cos B[/tex][tex]c^2=a^2+b^2-2ab\cos C[/tex]
Since we are asked to look for angle B, we will use
[tex]b^2=a^2+c^2-2ac\cos B[/tex]Given:
a = 12 cm
b = 8 cm
c = 15 cm
Substituting the given values to our equation:
[tex]b^2=a^2+c^2-2ac\cos B[/tex][tex](8)^2=(12)^2+(15)^2-2(12)(15)\cos B[/tex][tex]64=144+225-(360)\cos B[/tex][tex]360\cos B=369-64[/tex][tex]360\cos B=305[/tex][tex]\frac{360\cos B}{360}=\frac{305}{360}[/tex][tex]B=\cos ^{-1}\frac{305}{360}[/tex][tex]B=32.089[/tex]Since we are asked to round the answer to its nearest tenth, the final answer would be 32.1 degrees.
How many millimeters are there in 16 meters?A. 160 millimetersB. 1,600 millimetersC. 160,000 millinersD. 16,000 millimeters
It is known that 1 meter = 1000millimeter.
Therefore, 16 meters = 16X 1000 millimeters
16 meters = 16, 000 millimeters.
Hence, option D is the correct answer.
what is the vertex of y=2(x-3)^2+6 and determine if it’s maximum or minimum value
The general equation of a vertex of a parabola is given by
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where} \\ \text{The coordianates of the vertex are} \\ (h,k) \end{gathered}[/tex]If we compare the general equation with that given in question 2
[tex]y=2(x-3)^2+6[/tex]We can infer that
[tex]\begin{gathered} -h=-3 \\ \text{Hence} \\ h=3 \\ \text{Also} \\ k=6 \end{gathered}[/tex]Thus, the vertex is
[tex](h,k)=(3,6)[/tex]To determine if it is maxima or minima, we will use the graph plot
We can observe that we have a minimum value.
Usually, we can determine this also from the value of a.
If a is negative, we have a maxima
If a is positive, we have a minimum
The value of a =2 (Positive)
Hence, we have a minimum
Determine if (−2,4) is a solution to the following system of inequalities.-3x > -7y -37x > -5y -4
Remember that ordered pairs are written in the form (x,y).
Then, to check if (-2,4) is a solution to the system of inequalities, both of the given inequalities should be verified when replacing x=-2 and y=4.
Replace x=-2 and y=4 into the inequalities and check if both of them are satisfied or not.
-3x > -7y - 3
[tex]\begin{gathered} \Rightarrow-3(-2)>-7(4)-3 \\ \Rightarrow6>-28-3 \\ \Rightarrow6>-31 \end{gathered}[/tex]Sice 6 is greater than -31, then this inequality is satisfied by (-2,4).
7x > -5y-4
[tex]\begin{gathered} \Rightarrow7(-2)>-5(4)-4 \\ \Rightarrow-14>-20-4 \\ \Rightarrow-14>-24 \end{gathered}[/tex]Since -14 is greater than -24, then this inequality is satisfied by (-2,4).
Since both inequalities are satisfied by (-2,4) then (-2,4) is a solution to the given system of inequalities.
Add.−4+ (-4) = Adding negative numbers
Solution
- The solution steps are given below:
[tex]\begin{gathered} -4+(-4)= \\ -4-4=-8 \end{gathered}[/tex]Answer
The answer is -8
The tables of ordered pairs represent some points on the graphs of Lines F and G.
Line F
x y
2 7
4 10.5
7 15.75
11 22.75
Line G
x y
-3 4
-2 0
1 -12
4 -24
Which system of equations represents Lines F and G?
1. y=1.75x+3.5
y=-4x-8
2. same as 1 but -8 is -2
3. 1.75 and 3.5 are switched
4. 2 and 3 combined
In linear equation, Equation for line F is y = 1.75x + 3.5 and equation for line G is y = -4x-8.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).y = 1.75x + 3.5 (For line F)
let's take the point (2,7) and put in the equation,
y = 1.75*2 + 3.5
= 3.5 +0.35
= 7
which is true.
Hence, (2,7) satisfies the equation.
y = -4x-8 (For line G)
lets take the point (-3,4) and put in the equation,
y = (-4)*(3) - 8
= 12 - 8
= 4
which is true.
Hence, (-3,4) satisfies the equation.
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What is the value of the expression below when x = 5 and y 5? 6x — бу
We want to find the value of the given expression;
[tex]6x-6y[/tex]When x=5 and y=5;
Substituting these values in, we have;
[tex]\begin{gathered} 6(5)-6(5) \\ =30-30 \\ =0 \end{gathered}[/tex]Therefore, the answer to this question is zero.
HELP! I need this ASAP!!A recursive rule for a sequence is given. Find the first four terms of the sequence. f(1) =5 f(n)= f(n-1) +3, where n is an integer and n ≥ 2
f(n) = f(n-1) + 3
substitute n= 2 in the above
f(2) = f (2-1) + 3
= f(1) + 3
= 5 + 3
= 8
substitute n = 3 in the formula
f(3) = f(3-1) + 3
= f(2) + 3
= 8 + 3
= 11
substituite n = 4
f(4) = f(4-1) + 3
= f(3) + 3
= 11 + 3
= 14
The first four terms are 5, 8, 11 and 14
21= ______hL how many hL
We want to convert litres L to Hectolitres hL.
[tex]1L=0.01L[/tex]one litre equals 0.01 hectolitre.
So, to convert 2L to hL, we have;
[tex]\begin{gathered} 1L=0.01L \\ 2L=0.02L \end{gathered}[/tex]The fancy restaurant Mackenzie atel at was having asale so her dinner was 80% of the original cost. Theoriginal cost of her dinner was $20.00. What is the saleprice?
Given data:
The original cost of dinner C=$20.00.
The sale price is 80% of the original cost.
[tex]\begin{gathered} S=\frac{80}{100}(20)_{} \\ =0.8(20) \\ =16 \end{gathered}[/tex]Thus, the final sale price is $16.00.
A volcano on a recently discovered planet rises to a height of 22.187 mi. Use the table of facts to find the height of the volcano in feet. Round your answer to the nearest tenth.
22.187 mi
1 mi = 5280 ft
22.187 mi = 22.187 x 5280 ft = =117147.36 ft
Answer:
117,147.36 ft
Write the English sentence as an equation in two variables. Then graph the equation.The y-value is three less than twice the X-value.
Given the sentence:
The y-value is three less than twice the X-value.
Let's write the sentence as an equation then graph the equation.
The equation that represents the sentence is:
y = 2x - 3
To graph the eqautaion, let's find and plot three points, then connect the points using a straight edge.
• When x = 1:
Substitute 1 for x and solve for y.
y = 2(1) - 3
y = -1
• When x = 2:
Substitute 2 for x and solve for y.
y = 2(2) - 3
y = 4 - 3
y = 1
• When x = 3:
Substitute 3 for x and solve for y.
y = 2(3) - 3
y = 6 - 3
y = 3
• When x = 0:
y = 2(0) - 3
y = -3
Thus, we have the points:
(1, -1), (2, 1), (0, -3), and (3, 3)
The graph is attached below.
ANSWER:
Equation: y = 2x - 3
Write an equation in slope-intercept form for the line with slope-2 and y-intercept 3.
Answer:
wait I will do it
Step-by-step explanation:
i will sent it after sometimes
Hi i need help finding the answer? If you could helpMe out?
Given:
Given a figure.
The side of the square is 8.
The radius of the semicirles is 4.
Required:
To find the perimeter of the given figure.
Explanation:
Here the circumference is
[tex]\begin{gathered} =2\pi r \\ \\ =2\times3.14\times4 \\ \\ =25.12 \end{gathered}[/tex]Now the perimeter is
[tex]\begin{gathered} =25.12\times2 \\ =50.24 \end{gathered}[/tex]Final Answer:
The perimeter of the given figure is 50.24 inches.
measures of relative position
Arranging the diameter in the ascending order,
1.31, 1.31, 1.33, 1.36, 1.43, 1.47, 1.48, 1.49, 1.49, 1.53, 1.53, 1.53, 1.58, 1.68, 1.69.
There are 15 data entry in the given data set.
The 78th percentile can be determined as,
[tex]15\times\frac{78}{100}=11.7[/tex]Thus, the 12th data entry in the ascending order has 78th percentile. 1.53 is the required diameter.
Given: GEFH is a parallelogram with two 35° angles as shown.EF35359GHWhich is the most specific descriptor for GEFH?ParallelogramRhombusRectangleSquare
SOLUTION
The diagram above satifies all the properties of a parallologram
Which are
[tex]\begin{gathered} \text{opposite angle are equal} \\ \text{Opposite sides are equal and parallel} \\ \text{adjacent angle are supplementary} \end{gathered}[/tex]But if from the rule of isoseleses triagle we can conclude that all the side of the figure above are equal
Hence the most specific description for GEFH is
[tex]\text{Rhombus}[/tex]Last year, Milan had $10,000 to invest. He invested some of it in an account that paid 6% simple interests per year, and he invested the rest in an account that paid 9% simple interest per year. After one year, he received a total of $840 in interest. How much did he invest in each account?
Let's define the next variables
x: amount of money invested in one account
y: amount of money invested in the other account
Milan had $10,000 to invest, then
x + y = 10000 (eq. 1)
The interest Milan gets after one year are: 0.06x and 0.09y. He received a total of $840 in interest, then
0.06x + 0.09y = 840 (eq. 2)
Isolating x from equation 1:
x = 10000 - y
Replacing this result into equation 2,
0.06(10000 - y) + 0.09y = 840
0.06(10000) - 0.06(y) + 0.09y = 840
600 + 0.03y = 840
0.03y = 840 -600
0.03y = 240
y = 240/0.03
y = 8000
Then,
x = 10000 - y
x = 10000 - 8000
x = 2000
He invested $2000 in the account that paid 6% simple interests per year and $8000 in the account that paid 9% simple interests per year
If f(x) = x, the inverse off, f-1 could be represented by
Solution
For this case we have the following function given:
y=f(x)= x
And we want to find the inverse so we can do the following steps:
1) replace y with x
x= y
2) solve for y
y = x
Then the folution would be:
A) f-1 (x) =x
The type and number of fish caught in the Charleston Harbor in March was recorded for a month. The results are recorded in the table below. Whatis the probability that the next fish caught is a drum or a flounder? Enter a fraction or round your answer to 4 decimal places, if necessary.Flounder262Number of Fish Caught in MarchBlack DrumBluefish336Red Drum382181Sea Trout190
1) The first thing we need to do in this question, is to find the sample space, i.e. the total number of outcomes, in this case, fishes.
[tex]262+382+181+336+190=1351[/tex]2) Since no one could pick simultaneously two types of fish, then we can tell that these events are mutually exclusive. So, we can write the following:
[tex]\begin{gathered} P(flounder)=\frac{262}{1351} \\ \\ P(black\:drum)=\frac{181}{1351} \\ \\ P(red\:drum)=\frac{382}{1351} \\ \\ P(drum\:or\:flounder)=\frac{262}{1351}+\frac{181}{1351}+\frac{382}{1351}=\frac{825}{1351}\approx0.6107 \end{gathered}[/tex]Note that by "drum" we are including black and red drum.
That is the answer.
If 5% of a certain number is -62/3
the number is
Could I please get some help on my homework for the next question like this please
we have the equations
x^2+y^2=9
this is the equation of a circle centered at the origin with a radius of 3 units
y=x
this is the equation of a line
therefore
The total points of intersection are 2see the figure below to better understand the problem16. Which expression shows how to use the Distributive Property to solve 6 x 349? A) (6 x 300) x (6 x 40) x (6 x 9) B) (6 + 300) + (6 + 40) + (6 + 9) C) (6 x 3) + (6 x 4) + (6 x 9) D) (6 x 300) + (6 x 40) + (6 x 9)
since 349 can be also written as 300+40+9
write the number like so in the multiplication
[tex]6\cdot349=6\cdot(300+40+9)[/tex]apply the distributive property
[tex](6\cdot300)+(6\cdot40)+(6\cdot9)[/tex]Two sides of a triangle have the same length. The third side measures 3 m less than twice the common length. The perimeter of the triangle is 17 m. What are the lengths of the three sides? What is the length of the two sides that have the same length? m
Let the common sides have length x, i.e, we have 2 sides measuring x
the third side would measure 2x - 3.
The perimeter = x + x + 2x - 3 = 4x - 3 = 17
so, 4x = 17 + 3 ,
4x = 20
x = 20/4 = 5m
Therefore, the three sides are 5m , 5m and 2( 5 )-3 = 10 - 3 = 7m
Find the amount of each payment R for a t= 18 year loan with principal P = $18,000 and interest rate r = 9% compounded monthly. Round your final answer to two decimal places.
The amount of each payment to 2 decimal places = $90406.80
Explanation:
t = 18 year
Principal = P = $18,000
r = 9% 0.09
Using compound interest formula:
[tex]FV\text{ = P(1 + }\frac{r}{n})^{nt}[/tex]n = number of times it was compounded in a year.
since it is monthly, n = 12
[tex]\begin{gathered} FV\text{ =future value} \\ FV\text{ = 18000(1+ }\frac{0.09}{12})^{12\times18} \end{gathered}[/tex][tex]\begin{gathered} FV=18000(1+0.0075)^{216} \\ FV\text{ = }18000(1.0075)^{216} \\ FV\text{ = 18000}\times5.0226 \\ FV\text{ = 90406.8} \end{gathered}[/tex]The amount of each payment to 2 decimal places = $90406.80
when f(x)=-3(2)^-× what is the value of f(-3)
Let the function be,
[tex]f(x)=3\times2^{-x}[/tex]Put -3 for x in the function to find f(-3) implies,
[tex]\begin{gathered} f(-3)=3\times2^{-(-3)} \\ =3\times2^3 \\ =3\times8 \\ =24 \end{gathered}[/tex]Thus, f(-3) is 24.
Find the value of x. Assume that segments that appear to be tangent are tangent. 12, x , 6
The value of x is 16.64.
Given that 14 is tangent to the circle and 9 is a radius, this is a right triangle.
From the figure, we have
Using the Pythagoras theorem,
a^2 +b^2 =c^2
9^2+14^2 =x^2
81+196 = x^2
277 = x^2
By taking the square root of each side, we get
sqrt(277) = sqrt(x^2)
sqrt(277) =x
x = 16.64
Pythagoras theorem:
The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle. Here, examples help to demonstrate the formula and proof of this theorem. In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulas.
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Can you help me i need the answers
Given that
The figure is given on the coordinate plane. And we have to find the vertices of the figure after a 90-degree clockwise rotation.
Explanation -
So the figure will be rotated from its position clockwise as
Since the given points are J(-9, -8)
K(-2, -8)
L(-2, -3)
M(-9, -3)
After rotating the points will be
J(
K(-7, -3)
L(-2, -3)
M(-2, 4)