The Solution.
First, we shall convert the given lengths to inches.
[tex]undefined[/tex]How do I turn 19/40 in to a % thanks
multiply the expression by 100 to make it into percentage :
[tex]\begin{gathered} \frac{19}{40\text{ into percenatge }}\text{= 0.475}\times100\text{ } \\ \\ \frac{19}{40\text{ into percenatge }}\text{== 0.475}\times100 \\ \frac{19}{40\text{ into percenatge }}\text{= 47.5\%} \end{gathered}[/tex]Answer : 47.5 %
Simplify the square root:square root of negative 72 end rootAnswer choices Include:2 i square root of 186 i square root of 218 i square root of 22 i square root of 6
We need to simplify the next square root:
[tex]\sqrt[]{-72}[/tex]First, we need to rewrite the expression as:
[tex]\sqrt{-72}=\sqrt[]{-1}\ast\sqrt[]{72}[/tex]Where √-1 = i
Therefore:
[tex]\sqrt{-1}\ast\sqrt{72}=\sqrt[]{72}\text{ i}[/tex]Finally, we can simplify inside of the square root:
[tex]\sqrt[]{72}i=\sqrt{6\ast6\ast2}i=\sqrt{6^2\ast2}i=6i\sqrt[]{2}^[/tex]Therefore, the correct answer is "6 i square root of 2".
Convert the radian measure to degreemeasure. Then, calculate the arc length thatcorresponds to a circle with a 35-centimeterdiameter. Round your answer to the nearesttenth.
We will have the following:
First,:
[tex]\frac{4\pi}{15}=\frac{4\pi}{15}\ast\frac{180}{\pi}=48[/tex]Then, the arc length will be:
[tex]\begin{gathered} s=(\frac{15}{2})(\frac{4\pi}{15})\Rightarrow s=2\pi \\ \\ \Rightarrow s\approx6.3 \end{gathered}[/tex]So, the arc length is approximately 6.3 cm.
How much do I need to increase a radius of a circle to increase it's area 10 times?
Given that
It is said that we have to find the amount by which the radius will be increased such that the area is increased by 10 times.
Explanation -
The formula for the area of the circle is given as
[tex]\begin{gathered} Area=\pi\times r^2 \\ \\ A=\pi r^2-----------(i) \\ \\ where\text{ r is the radius of the circle.} \end{gathered}[/tex]Now the new area is 10 times the previous one.
Let the new area be A' and the new radius be R.
Then,
[tex]\begin{gathered} A^{\prime}=\pi\times R^2 \\ \\ As\text{ A'=10}\times A \\ \\ Then\text{ substituting the value of A' we have} \\ \\ 10\times A=\pi\times R^2 \end{gathered}[/tex]Now again substituting the value of A we have
[tex]\begin{gathered} \pi\times R^2=10\times\pi\times r^2 \\ \\ R^2=10r^2 \\ \\ R=\sqrt{10}\times r \end{gathered}[/tex]Hence the new radius will be √10 times the initial radius such that the area gets increased by 10 times.
Final answer - Therefore the final answer is √10 times.
17. What is the value of x in the rhombusbelow?AC(x+40)B3x"D
Remember that
In a rhombus, diagonals bisect each other at right angles (perpendicular)
so
that means
(x+40)+(3x) =90 degrees ---------> by complementary angles
solve for x
4x+40=90
4x=90-40
4x=50
x=12.5find the answer fast pleaseee
Answer: (2 · (-4y)) + (2 · 2x) + (2 · (-3))
Step-by-step explanation: Distribute the 2 by multiplying each term in the parentheses by 2.
Find the lengths of the diagonals of rectangle WXY Z where WY-2x + 34 and XZ = 3x – 26The length of each diagonal isunits.
To solve the exercise, you can first draw a picture to better understand the statement. So,
Now, in a rectangle, the lengths of the diagonals measure the same. So,
[tex]\begin{gathered} WY=XZ \\ -2x+34=3x-26 \end{gathered}[/tex]To solve for x first subtract 34 from both sides of the equation
[tex]\begin{gathered} -2x+34-34=3x-26-34 \\ -2x=3x-60 \end{gathered}[/tex]Subtract 3x from both sides of the equation
[tex]\begin{gathered} -2x-3x=3x-60-3x \\ -5x=-60 \end{gathered}[/tex]Divide by -5 into both sides of the equation
[tex]\begin{gathered} \frac{-5x}{-5}=\frac{-60}{-5} \\ x=12 \end{gathered}[/tex]Finally, replace the value of x in the length of any of the diagonals, for example, the diagonal WY
[tex]\begin{gathered} WY=-2x+34 \\ WY=-2(12)+34 \\ WY=-24+34 \\ WY=10 \end{gathered}[/tex]Therefore, the length of each diagonal is 10 units.
In the diagram below of parallelogram ROCK,mZC is 70° and mZROS is 65º.Oс70%650RSK.What is mZKSO?
Answer:
∠KSO = 135°
Explanation:
On a parallelogram, the opposite angles have the same measure. It means that the measure of ∠R is:
∠R = ∠C
∠R = 70°
On the other hand, the sum of the interior angles of a triangle is equal to 180°, so we can calculate the measure of ∠RSO as:
∠RSO = 180 - ∠ROS - ∠R
∠RSO = 180 - 65 - 70
∠RSO = 45°
Because the angles RSO, ROS, and R form the triangle ROS.
Finally, ∠RSO and ∠KSO form a straight line, so their sum is equal to 180°. Then, we can calculate ∠KSO as:
∠KSO = 180 - ∠RSO
∠KSO = 180 - 45
∠KSO = 135°
Then, the answer is 135°
f(x) = 2.5x - 10.5if X= 2
Answer:
-5.5
Explanation:
Gven the below function;
[tex]f(x)=2.5x-10.5[/tex]when x = 2, it means we should substitute x = 2 into the above function or find f(2);
[tex]\begin{gathered} f(2)=2.5(2)-10.5 \\ =5-10.5 \\ =-5.5 \\ \therefore f(2)=-5.5 \end{gathered}[/tex]in the diagram, AB=9, DB=5, and BC=12. if m< B = 90, what is the perimeter of ADC ?
To answer this question, we can draw the triangle as follows:
We can start answering this question, finding the value of the side AC (one of the sides of the triangle ADC (not shown)). Then, we can apply the Pythagorean Theorem to find AC (the hypotenuse in this case). Thus, we have:
[tex]AC^2=AB^2+BC^2\Rightarrow AC^2=(9)^2+(12)^2=81+144[/tex]Then, we have:
[tex]AC^2=225\Rightarrow\sqrt[]{AC^2}=\sqrt[]{225}\Rightarrow AC=15[/tex]Then, the measure of the side AC = 15.
Now, we need to find the measure of the side DC. We can also need to apply the Pythagorean Theorem to find it:
We have that DB = 5, and BC = 12. Then:
[tex]DC^2=DB^2+BC^2=5^2+12^2=25+144\Rightarrow DC^2=169[/tex]Now, we need to take the square root to both sides of the expression to solve for DC:
[tex]\sqrt[]{DC^2}=\sqrt[]{169}\Rightarrow DC=13[/tex]To find the perimeter of the triangle ADC, we have:
1. AD = AB - DB ---> AD = 9 - 5 ---> AD = 4 (we deduce this from the given data in the question.)
2. AC = 15 (found in the first step using the Pythagorean Theorem.)
3. DC = 13 ((found in the second step using the Pythagorean Theorem.)
Therefore, the perimeter of the triangle ADC is the sum of all of its sides, then, we have:
[tex]P_{\text{trangleADC}}=AD+AC+DC\Rightarrow P_{triangleADC}=4+15+13=32[/tex]Therefore, the perimeter of the triangle ADC is equal to 32 units.
(We can apply the Pythagorean Theorem twice since we have a right triangle in both cases: triangle ABC and triangle DBC.)
equation or special characters
Inverse table.
- What undoes sine?
writen as:
[tex]\sin ^{-1}[/tex]called: inverse sine
also called: arcsine
- What undoes cosine?
written as
[tex]\cos ^{-1}[/tex]called: inverse cosine
also called: arccosine
- What undoes tangent?
written as
[tex]\tan ^{-1}[/tex]called: inverse tangent
also called: arctangent
Table of sine, cosine, tangent for 30, 45 and 60 degrees.
Rachel is bowling with her friends. Her bowling ball has a radius of 4.1 inches. As she bowls she tracks the location of the finger hole above the ground. She starts tracking the location when the finger hole is at the 12 o'clock position and she notices that she got some backspin on the ball and it rotates counter-clockwise.Write a function f that determines the height of the finger hole above the ground (in inches) in terms of the number of radians a the ball has rotated since she started tracking the finger hole. (Note that aa is a number of radians swept out from the 12-o'clock position.)f(a)=
Given that radius is r= 4.1 inches.
let track the location of finger hole is at 12 o'clock.
i.e. the angle is 0 degree.
at 12 o'clock
[tex]\theta=0[/tex]Now when the finger hole changed by 45 degree:
[tex]\theta=45[/tex]Now convert 45 degree into radians:
[tex]\begin{gathered} \theta=45\times\frac{\pi}{180} \\ \theta=\frac{\pi}{4} \end{gathered}[/tex]So angle is such that:
[tex]\begin{gathered} \theta\in\lbrack0,\frac{\pi}{4}\rbrack \\ 0\leq\theta\leq\frac{\pi}{4} \end{gathered}[/tex]Now calculate the measure of function in polar coordinates:
[tex]\begin{gathered} \theta=0,\text{ f(}\theta\text{)}=r \\ \theta=\frac{\pi}{2},\text{ f(}\theta)=r\cos \theta \end{gathered}[/tex]Taking measurement of function:
[tex]\begin{gathered} f(\theta)=r+r\cos \theta \\ f(\theta)=r(1+\cos \theta) \end{gathered}[/tex]So the function become and the limit is:
[tex]f(\theta)=r(1+\cos \theta),\text{ 0}\leq\theta\leq\frac{\pi}{4}[/tex]#5There are 357 students at Rydell MiddleSchool. The students were asked to choosetheir favorite class. Of the 21 students inHomeroom A, 8 students chose CSI as theirfavorite. Based on these results, how manyof the students in Rydell Middle Schoolwould you expect to choose CSI as theirfavorite class?
We could write the following proportion and then solve for x:
Therefore, we could expect that 136 students chose CSI as their favorite class in Rydell Middle School.
ine temperaturtemperature at midnight?-53Allie scores 4 points in the first round of a card game. In the next round, she loses 6 points. Then she scores 4more points. How many points does Allie have after three rounds?on
3
Allie scores 4 points in the first round of a card game. In the next round, she loses 6 points. Then she scores 4.
How many points does Allie have after three rounds?
First round: 4 points (positive)
Second round = lose 6 points (negative)
Third round = scores 4 (positive )
Add and subtract all the points
4-6+4 = 2
Answer the questions below.(a)The 10 members of the swim team completed the following numbers of laps at today's practice: 78,79,81,82,84,85,86,87,88,89.Which measure should be used to summarize the data?MeanMedianMode(b)A car dealer has used cars for sale for the following amounts: $3400,$3600,$3700,$3800,$3900,$4000,$4100,$4300,$7600.Which measure should be used to summarize the data?MeanMedianMode(c)A data set shows the age of each resident at Lakeview Retirement Home.Which measure gives the age shared by the most residents?MeanMedianMode
Answer
Explanation
(a) The first step is to arrange the numbers of laps in ascending order:
78, 79, 81, 82, 84, 85, 86, 87, 88, 89.
Lucy you will use more than one out of two half s cup but less than one whole cup of flour for a recipe what fraction of a cup might lessy use explain
Given:
Leslie will use more than ½ cup but less than 1 whole cup of flour for a recipe.
Let's find the fraction of a cup Leslie might use.
To find the fraction of a cup Leslie might use, find the fraction that is less than 1 whole and still more than ½.
To find the fraction of a cup Leslie might use, we have the fraction:
[tex]\frac{3}{4}[/tex]This is because the fraction, ¾, is less than 1 whole and it is still more than ½.
¾ is ¼ less than 1 whole and ¼ greater than ½
Therefore, the fraction of a cup Leslie might use is ¾
ANSWER:
[tex]\frac{3}{4}[/tex]2. Write the equation of g(x) given the table below. X -2 --1 1 g(x) 3 6 12
let us first calculate the slope:
[tex]m=\frac{6-3}{-1--2}=\frac{3}{1}=3[/tex]having the slope, we can use the slope-point equation and we get that
[tex]\begin{gathered} y-12=3(x-1)=3x-3 \\ y=3x-3+12=3x+9 \end{gathered}[/tex]so g(x)=3x+9
Which points are separated by a distance of 6 units? O A. (2, 4) (2, 2) B. (1,8) (1,2) c. (3, 1) (3,6) D. (5,6) (5,5)
Recall that the distance formula is given by
[tex]d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}[/tex]We are asked to find out which of the given points have a distance of 6 units?
Let us analyze each option.
A. (2, 4) (2, 2)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({2-2_{}})^2+({2-4})^2} \\ d=\sqrt[]{({0})^2+({-2})^2} \\ d=\sqrt[]{4}^{} \\ d=2 \end{gathered}[/tex]Option A does not have a distance of 6 units, so it is not the correct option.
B. (1,8) (1,2)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({1-1})^2+({2-8})^2} \\ d=\sqrt[]{({0})^2+({-6})^2} \\ d=\sqrt[]{36}^{} \\ d=6 \end{gathered}[/tex]As you can see, the distance between these points is exactly 6 units.
Therefore, Option B is the correct answer.
c. (3, 1) (3,6)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({3-3})^2+({6-1})^2} \\ d=\sqrt[]{(0)^2+({5})^2} \\ d=\sqrt[]{25} \\ d=5 \end{gathered}[/tex]Option C does not have a distance of 6 units, so it is not the correct option.
D. (5,6) (5,5)
[tex]\begin{gathered} d=\sqrt[]{({x_2-x_1})^2+({y_2-y_1})^2} \\ d=\sqrt[]{({5-5})^2+({5-6})^2} \\ d=\sqrt[]{({0})^2+({-1})^2} \\ d=\sqrt[]{1}^{} \\ d=1 \end{gathered}[/tex]Option D does not have a distance of 6 units, so it is not the correct option.
an 20. Dequan spent 44 minutes yesterday cleaning 3 bathrooms and the kitchen at home. He spent the same amount of time cleaning each place, and then 8 minutes putting all the supplies away after. Write an algebraic equation and then solve to find out how many minutes m he spent on each room.
Let:
b = minutes spent cleaning the 3 bathrooms
k = minutes spend cleaning the kitchen
He spent the same amount of time cleaning each place, therefore:
k = b
He spent 44 minutes in total, besides he spent 8 minutes putting all the supplies away after:
b + k + 8 = 44
since k = b = m:
m + m + 8 = 44
2m + 8 = 44
Solving for m:
2m = 44 - 8
2m = 36
m = 36/2
m = 18
Therefore, he spent 18 minutes in each room
.The balance on Mr. Finch's credit card is -$210. It is 3 times the balance on Mr. Nguyen's credit card. Find the quotient -210 ÷ 3 and explain what it means in this context.
Given: Balance of Finch's card is = -$210.
This is 3 times the balance on Mr. Nguyen's credit card.
To find: -210/3.
Explanation:
Let the balance on Mr. Nguyn's card be = x.
The balance of Mr. Finch's card is 3 times Mr. Nguyen's card.
Mathematically this can be expressed as:
[tex]-210=3x[/tex]Now, the value of x or "Mr. Nguyen's credit card balance" can be calculated as:
[tex]\begin{gathered} x=\frac{-210}{3} \\ x=-70 \end{gathered}[/tex]Therefore, the term -210/3 represents Mr. Nguyen's credit card balance and its value is -$70.
Final Answer: The term -210/3 represents Mr. Nguyen's credit card balance and its value is -$70.
How does linear inequality work?
To graph a inequality we first need to grapg the equality, in this case the line y=3-1/3x, and then we check which of the two sets of points fullfil the inequality and paint this set. in this case the inequality is estrict so it doesn't include the boundary line.
10. A system of equations is shown below.3x - y = 10y = 4x-8What is the value of x - y of the solution to the system?C. 14A -98D. 62B-18
Given:
3x - y = 10
y = 4x-8
Required:
What is the value of x - y of the solution to the system?
Explanation:
3x - y = 10
y = 4x-8
substitute into one of the equations
[tex]\begin{gathered} 3x-(4x-8)=10 \\ \\ combine\text{ like terms} \\ \\ -x+8=10 \\ \\ -x=2 \\ \\ x=-2 \end{gathered}[/tex][tex]\begin{gathered} substitute\text{ value of x} \\ \\ 3\times(-2)-y=10 \\ \\ -6-y=10 \\ \\ -y=10+6 \\ \\ -y=16 \\ \\ y=-16 \end{gathered}[/tex][tex]\begin{gathered} substitute\text{ value into x-y:} \\ \\ -2-(-16) \\ \\ -2+16 \\ \\ 14 \end{gathered}[/tex]Required answer:
C. 14
Use trig ratios to find the missing side of the triangle below. Show all of your work. Round your answer to the nearest 10th.
Answer:
[tex]x\approx12.7[/tex]Step-by-step explanation:
To solve this situation, we can use trigonometric ratios or relationships to find x. Trigonometric ratios are represented by the following diagram and formulas:
Therefore, to find x, use the sen relationship:
[tex]\begin{gathered} \sin (65)=\frac{x}{14} \\ x=14\cdot\sin (65) \\ x=12.688 \\ \text{ Rounding to the nearest 10th:} \\ x\approx12.7 \end{gathered}[/tex]which statement describes the sequence -9,-3,3,9,15,
This sequence can be represented by the following formula:
an = 3(2n - 5)
n ∈ N
find the smallest non negative value for x in degrees that makes the equation cot (x) = 0 true.
It is given that,
cot (x) = 0
To find the smallest non-negative value for x in degrees:
So that,
[tex]\begin{gathered} \cot (x)=0 \\ \cot (x)=\cot (90^{\circ}) \\ x=90^{\circ} \end{gathered}[/tex]Hence, the smallest value of x is 90 degrees.
What are the Characteristics for rhombus
The characteristics of a rhombus are the following:
• Opposite sides are parallel ang congruent (equal)
,• The diagonal lines are bisectors (they cut in half) the internal angles
,• The two diagonals have different legths (usually represented by d and D)
,• The point where the two diagonals meet is the center of the rhombus
Which values of x would make a polynomial equal to zero if the factors of thepolynomial were (x+6) and (x+9)?
Given
(x+6) and (x+9) are the factors of a polynomial.
To find: Which values of x would make a polynomial equal to zero?
Explanation:
It is given that,
(x+6) and (x+9) are the factors of a polynomial.
Then, the polynomial can be written as,
[tex]p(x)=(x+6)(x+9)[/tex]Also, if (x+a) is a factor of a polynomial p(x).
Then, p(-a)=0.
Therefore,
For the factors (x+6) and (x+9),
The polynomial p(x) is zero at x=-6, and x=-9.
Hence, the answer is x = -6, -9.
what is a division expression with a quotient that is greater than 8 divided by 0.001
SOLUTION
Write out the given expression
[tex]\frac{8}{0.001}[/tex]An expression with a quotient that is greater than the expression above is to increase the numerator and leave the denominator unchanged
Hence, we have
[tex]\frac{9}{0.001}is\text{ greater than }\frac{8}{0.001}[/tex]Therefore
The division expression with a quotient that is greater than 8 divided by 0.001 is
9/0.001
In January, it snowed 36.45 inches. In December it snowed 19.7 inches. How many more inches did it snow in January than in December?
Determine the difference in height of snow.
[tex]\begin{gathered} h=36.45-19.7 \\ =16.75 \end{gathered}[/tex]Thus, 16.75 inches more snowed in
If you select one card at random from a standard deck of 52 cards, what is the probability that the card is black OR a 6?
Since there are 52 cards in the standard deck
Since half of them are in black
Then the probability of getting a black card is
[tex]\begin{gathered} P(b)=\frac{\frac{52}{2}}{52} \\ P(b)=\frac{26}{52} \end{gathered}[/tex]Since there are 4 cards of 6, then
The probability of getting 6 is
[tex]P(6)=\frac{4}{52}[/tex]OR in probability means adding, then
The probability of getting a black card or a 6 is
[tex]\begin{gathered} P(b\text{ or 6)=}\frac{26}{52}+\frac{4}{52} \\ P(b\text{ or 6) =}\frac{30}{52} \end{gathered}[/tex]We can simplify it by dividing up and down by 2
[tex]\begin{gathered} P(b\text{ or 6)=}\frac{\frac{30}{2}}{\frac{52}{2}} \\ P(b\text{ or 6)=}\frac{15}{26} \end{gathered}[/tex]The answer is P(b or 6) = 30/52 OR 15/26