We have the next formula to calculate the distance between 2 points
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]in our case
(0,10)=(x1,y1)
(-9,1)=(x2,y2)
we substitute the values
[tex]d=\sqrt[]{(1-10)^2+(-9-0)^2}[/tex]then we simplify
[tex]d=9\sqrt[]{2}=12.7279[/tex]Therefore the correct choice is B. 12.73
How many days did Amelia record the the time she spent working in the yard ? Step
SOLUTION:
7) The times recorded, you count the number of strokes. Total number of strokes = 5 strokes.
8)
fractions (1/4, 3/4, 6/4, 6/4, 6/4)
[tex]\begin{gathered} \frac{1}{4}+\text{ }\frac{3}{4}+\text{ 1}\frac{2}{4}+\text{ 1}\frac{2}{4}+\text{ 1}\frac{2}{4} \\ \text{Total whole number= 1+1+1= 3} \\ \text{Total fractions= }\frac{1}{4}+\frac{3}{4}+\frac{2}{4}+\frac{2}{4}+\frac{2}{4} \\ \text{Total fractions= }\frac{1+3+2+2+2}{4} \\ T\text{otal fractions= }\frac{10}{4} \\ \text{otal fractions= 2}\frac{2}{4}\text{ OR 2}\frac{1}{2}\text{ hours} \end{gathered}[/tex][tex]\begin{gathered} \text{Total hours: 2+2}\frac{1}{2} \\ \text{Total hours: 5}\frac{1}{2}\text{ hours} \end{gathered}[/tex]9) To calculate the average hours. We add all the hours and divide by 5
[tex]\begin{gathered} 5\frac{1}{2}\div5 \\ \frac{11}{2}\div\frac{5}{1} \\ \frac{11}{2}\times\frac{1}{5} \\ \frac{11}{10} \\ 1\frac{1}{10}\text{ hours} \end{gathered}[/tex]Final answers:
7) 5 days
8) 5 and half hours
9) 1 and tenth hours
write an equation to describe the relationship between T and the number of tickets and seeds in the total cost of tickets
c = 55t
Explanation:To find the relationship between the cost (c) and the number of ticket (t), the first thing we do is find the rate of change
The rate of change = slope = change in c/change in t
using points (t, c): (2, 110) and (5, 275)
The rate of change = (275-110)/(5 - 2)
The rate of change = 165/3
The rate of change = 55
Using proportional equation:
y = kx
where k = constant of poroportionality
The equation:
y = kx
where y = cost of ticket = c
x = numer of tickets = t
k = constant of poroportionality = rate of change
k = 55
Our equation becomes:
c = kt
Th equation that describes the relationship:
c = 55t
Emily had 3 1/3 yards of rope. She bought an additional 75/6 yards of rope. How many total yardsof rope does Emily have?A. 121/8 yardsB. 111/8 yardsC. 101/3 yardsD. 101/8 yards
We will have to sum up the two yards
Which situation can be represented by this inequality? (7.10C, SS, RC2) 145 < 15n + 17 A Ann has made 15 necklaces. She will make 17 more necklaces every week. Ann makes necklaces for n weeks. For what values of n will Ann have made at most 145 necklaces? B Ann has made 17 necklaces. She will make 15 more necklaces every week. Ann makes necklaces for n weeks. For what values of n will Ann have made at most 145 necklaces? C Ann has made 15 necklaces. She will make 17 more necklaces every week. Ann makes necklaces for a weeks. For what values of n will Ann have made at least 145 necklaces? D Ann has made 17 necklaces. She will make 15 more necklaces every week. Ann makes necklaces for n weeks. For what values of n will Ann have made at least 145 necklaces?
Answer:
D. Ann has made 17 necklaces. She will make 15 more necklaces every week. Ann makes necklaces for n weeks. For what values of n will Ann have made at least 145 necklaces?
Explanation:
The inequality is:
145 ≤ 15n + 17
Then, the expression on the right side indicates that there is a fixed quantity of 17 and there is a variable quantity 15n that depends on the variable n. So, the situation that can represent this expression is that Ann has made 17 necklaces (fixed quantity) and she will make 15 more necklaces every week (a variable quantity).
So, if 15n + 17 represents the number of necklaces that Ann made after n weeks, the complete expression 145 ≤ 15n + 17 represents that this number of necklaces should be greater than or equal to 145.
Therefore, the correct answer is:
D. Ann has made 17 necklaces. She will make 15 more necklaces every week. Ann makes necklaces for n weeks. For what values of n will Ann have made at least 145 necklaces?
An octagon has a side length of 18 feet and an area of 806.4ft^2. find the area of a smaller octagon that has a side length of 15
Given side length is 15 feet
Area of octagon is:
[tex]A=2(1+\sqrt[]{2})a^2[/tex]Where
a = side length
so the area of this octagon is:
[tex]\begin{gathered} A=2(1+\sqrt[]{2})a^2 \\ =2(1+\sqrt[]{2})15^2 \\ =2\times(15)^2\times(1+\sqrt[]{2}) \\ =450(1+\sqrt[]{2}) \\ =1086.39 \end{gathered}[/tex]Pls read & answer the question then explain Brown your final answer to four decimal places do not round your intermediate computation
SOLUTION
Notice that there are 12 face cards
Also there are 13 diamond cards
The total number of cards is 52
Hence the probability of picking a face card and then a diamond card is:
[tex]\frac{12}{52}\times\frac{13}{52}[/tex]This gives
[tex]\frac{156}{2704}=0.0577[/tex]What is the sum of a number and its additive inverse?01012
The additive inverse of a number is the same number but in different signs.
For example, if the number is "a", the additive inverse will be "-a"
The sum of a number and its additive inverse will be :
[tex]a+(-a)=0[/tex]The answer is 0
what would Nate need to add to his model for it to be equivalent to Joe's model
Joe has the expression:
[tex]x+3\cdot1+2(-1)=x+3-2=x+1[/tex]And Nate has the expression:
[tex]x+4\cdot1=x+4[/tex]In order to have the same expression, Nate has to substract 3 units. This can be done by adding 3 "(-1)".
Then Nate would have:
[tex]x+4+3(-1)=x+4-3=x+1[/tex]Answer: 3 units of "-1" (Option C).
How to factor out the greatest common factor in a polynomial.
Factor 28x-98 by factoring out the greatest common factor.
Step-by-Step Solution
Step 1: Find the GCF of the terms of the polynomial.
28x=2 X 2 X 7 (x)
- 98=2 X 7(-7)
Answer:
14
Step-by-step explanation:
Which equation describes the circle having center point (4,2) and radius r = 3 in standard form? O A. (x-4)² + (y-2)² = 3 O B. (x+4)² + (x + 2)² = 9 Oc. (x+4)2 + (+ 2)2 =3 O D. (x-4)² + (x - 2)² =9
The correct option is
D. (x-4)^2 + (y-2)^2 = 9
The equation of a circle that has center in a point P = (h, k) is:
[tex](x-h)^2+(y-2)^2=r^2[/tex]Where r is the radius. In this case the center is in (4, 2). Then we can rplace h and k:
[tex](x-4)^2+(y-2)^2=r^2[/tex]All that is left is replace r by the radius. In this case r = 3 then r^2 = 9
Now we can complete the equation:
[tex](x-4)^2+(y-2)^2=9[/tex]And that's option D.
The Mosteller formula for approximating the surface area S, in square meters (m²), of a humanis given by the function below, where h is the person's height in centimeters and wis the person's weight in kilograms. According to this formula, ifa person's weight drops 20%, by what percentage does his or her surface area change?VhwS(h.w) -60Retblese aChoose the correct answer below.munic O A. It drops by approximately 10%.B. It drops by approximately 30%OC. It drops by approximately 20%.OD. It drops by approximately 40%.
Given the parameter in the question, we were asked to determine by what percentage does his or her surface area change.
Recall that:
Since surface area is a product of height and weight, a percentage of decrease in any of the parameter will give an equivalent percentage decrease.
From what is explained above, there will be approximately 20% drop.
The correct option is C, which is Drops by approximately 20%.
I need help what is 160 ÷7/8
Solve the division this way:
[tex]\frac{160}{\frac{7}{8}}=\frac{8\cdot160}{7}=182.86[/tex]The answer is 182.86
Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated.PMT = $7,500, interest is 4% compounded semiannually for 2 years Round the answer to nearest cent.
Given data:
PMT = $7,500
Interest rate = 4% or 0.04
Compounded semiannually = twice per year
Time = 2 years
Number of periods in total = 2 years x twice per year = 4 periods
interest rate per period = 0.04/2 = 0.02
The formula in getting the future value of an ordinary annuity is:
[tex]F=PMT(\frac{1+i)^n-1}{i})[/tex]where
i = interest rate per period
n = total number of periods
PMT = regular payment
From the given data above, let's substitute those in the formula.
[tex]\begin{gathered} F=7500\times\frac{(1+0.02)^4-1}{0.02} \\ F=7500\times\frac{1.02^4-1}{0.02} \\ F=7500\times\frac{0.08243216}{0.02} \\ F=7500\times4.121608 \\ F=30,912.06 \\ F\approx30,912.1 \end{gathered}[/tex]Ther
Put the following equation of a line into slope-intercept form, simplifying allfractions.2y - x = -8
Slope intercept form :
y=mx+b
Solving for y:
2y-x=-8
2y=-8+x
y= (-8+x)/2
y= -4+1/2x
y= 1/2x-4
Last week at a festival, a man sold 3 times as many tie-dyed t shirts as silk screened shirts. He sold 156 shirts altogether. How many tie-dyed shirts did he sale? The number of tie-dyed shirts is ?
Let us consider that the man sold x screened shirts.
Accordingly, he sold 3 times as many tie-dyed t shirts as silk screened shirts and he sold 156 shirts together.
Therefore,
[tex]\begin{gathered} 3x+x=156 \\ 4x=156 \\ x=39 \end{gathered}[/tex]Therefore, the number of silk screened shirts sold is 39.
So, the number of tie dyed shirts is
[tex]39\times3=117[/tex]Hence, The number of tie-dyed shirts is 117.
Given the function:7I <0f(x)={21 - 14 r > 0Calculate the following values:{(- 1) =f(0) ={(2) =
Given a function:
[tex]f(x)=\begin{cases}2x-7;\text{ }x<0 \\ 2x-14;x\ge0\end{cases}[/tex]We have to find the value of f(-1), f(0) and f(2).
It is known that the value of function is f(x) = 2x - 7 when x is less than zero. So, f(-1) is:
[tex]\begin{gathered} f(-1)=2(-1)-7 \\ f(-1)=-2-7 \\ f(-1)=-9 \end{gathered}[/tex]Thus, f(-1) = -9.
It is known that the value of the function is f(x) = 2x - 14 when x is equal to or greater than zero. So, f(0) is:
[tex]\begin{gathered} f(0)=2(0)-14 \\ f(0)=0-14 \\ f(0)=-14 \end{gathered}[/tex]Thus, f(0) = -14.
It is known that the value of the function is f(x) = 2x - 14 when is x is greater than zero. So, f(2) is:
[tex]\begin{gathered} f(2)=2(2)-14 \\ f(2)=4-14 \\ f(2)=-10 \end{gathered}[/tex]Thus, f(2) = -10.
Convert 3 7/8 into a decimal
We need to convert 3 7/8 to a decimal number
So,
[tex]\begin{gathered} 3\frac{7}{8}=3+\frac{7}{8} \\ \\ \frac{7}{8}=0.875 \\ \\ 3\frac{7}{8}=3+\frac{7}{8}=3+0.875=3.875 \end{gathered}[/tex]
Find the missing side lengths using trig ratios.61010у y29°BX ХVyaTo find the perimeter, you add all the side lengths. So, the perimeter of this triangle is
x=8.746, y=4.848 and 2P=23.594
1) Since we have the angles and the hypotenuse, we can find the missing legs by applying the following trigonometric ratios:
[tex]\begin{gathered} y=\sin (B) \\ y=\frac{opposite\text{ leg}}{\text{hypotenuse}} \\ y=\text{ sin(}29) \\ \frac{y}{10}=\sin (29) \\ y=10\cdot\sin (29) \\ y\approx4.848 \end{gathered}[/tex]2) For the missing leg x, we can write out in terms of the cosine (29) or sine (61)
[tex]\begin{gathered} \cos (29)=\frac{x}{10} \\ x=10\cdot\cos (29) \\ x\approx8.746 \end{gathered}[/tex]3) And finally, the Perimeter (2P) is equal to:
2P = 4.848 +8.746+10
2P=23.594
Rounding off to the nearest thousandth.
Which is the equation for the statement. The quotient of 1.2 added to a number and 5 is 3.6?A.) Z/1.2 + 5 = 3.6B.) Z + 5/1.2 = 3.6C.) (z+5)/1.2 = 3.6D.) (z + 1.2)/5 = 3.6
Let the number be Z
The quotient of point
Since the number is added to 5
z + 5 / 1.2 = 3.6
This implies that the number z added to 5 divided by 1.2 will give us a quotient
(Z + 5)/ 1.2 = 3.6
The answer is OPTION C
Which of the following inequalities is not true?|-9| < |9| -2²<30-7≤-51-11 ≥ 0
Recall that:
[tex]|a|=\begin{cases}a{\text{ if }a\geq0} \\ -a\text{ if }a<0\end{cases}.[/tex]Therefore:
[tex]|-9|=9=|9|.[/tex]Therefore the inequality:
[tex]|-9|<|9|[/tex]is not true.
Now, notice that:
[tex]\begin{gathered} -2^2=-4<0<3, \\ 0-7=-7\leq-5, \end{gathered}[/tex]Therefore the second and third inequalities are true.
Finally, notice that:
[tex]1-11=-10<0.[/tex]Therefore the last inequality is not true.
Answer: First and last inequalities.
which is an example of a remote i n t e r i o r angle of angle BCD
The two remote interior angles of ∠BCD are ∠CDE and ∠CED
By definition if we have a triangle with one of the base vertices extended outwards, then the remote interior angle are the opposite angles facing each other.
According to this question, the two remote interior angles of ∠BCD are ∠CDE and ∠CED
[tex]\angle BCD=\angle CDE+\angle CED[/tex]Please help I do not know how to do this
When two angles are called "Complementary Angles" it means their measures add up to 90 degrees.
Hence, if angle a and angle b are complementary angles,
The following data set represents the ACT scores for students in Mrs. Miller's collegewriting class. Use the data set to answer the question below.18 27 24 2229 21 23 2525 31 19 21What is the median ACT score for the class? (Round your answer to the nearesttenth, if necessary.)
Given: 18 27 24 22 29 21 23 25 25 31 19 21
The median is the middle number of the numbers given.
Lets arrange the numbers from smallet to largest:
18 19 21 27 21 22 23 24 25 25 29 31
From there we find the middle number by crossing out the numbers on both ends:
18 19 21 21 22 23 24 25 25 27 29 31
As you can see the number in the middle are 23 and 24 but we need one so we just find the number between 23 and 24 which is 23.5
Answer: Median is 23.5
Find the length of the radius. Identify the point of tangency, and enter the equation of the tangent line atthat point310ІВ10The radius of the circle is units, and the point of tangency isThe equation of a vertical line through this point is
The radius of the circle is from (0 to -2) on the plot, and it is:
[tex]\begin{gathered} 0-(-2) \\ 0+2 \\ 2\text{ units} \end{gathered}[/tex]The radius of the circle is 2 units
The point of tangency is the point where the straight line touches the circle:
And it is on the coordinate -2 on the x-axis and coordinate 0 on the y-axis
In coordinate geometry, the point of tangency is represented thus: (-2,0)
The equation of a vertical line through this point is
[tex]x=-2[/tex]Given the following function, F(x)=4x^2-16x+27, identify where the vertex would be?A. (-2,75)B. (-2,11)C.(2,11)D. (0,27)Need an explanation and answer!
we have the equation f(x) = 4x^2 - 16x + 27
Using the completing the square nethod
4x^2 -16x + 27
firstly, make sure the coefficient of x^2 is 1
divide all through by 4
4x^2/4 -16x/4 + 27/4
x^2 - 4x + 27/4 = 0
x^2 - 4x = -27/4
make the linear expression a perfect square
x^2 -4x/2 = -27/4
x^2 -(2x)^2 = -27/4
add the perfect square to both sides
x^2 -(2x)^2 = -27/4 + 4
(x - 2)^2 = -27/4 + 4
solving the Left hand side of the equation
-27/4 + 4
lcm is 4
-27 + 16/4/4
-11/4
(x - 2)^2 = -11/4
The vertex would lie when x = -2 and y =11
(-2 , 11)
The pair of square pyramids are similar. Use the given information to find the scale factorof the smaller square pyramid to the larger square pyramid.The scale factor is(Type whole numbers.)Enter your answer in each of the answer boxes.
Write out the given volume
[tex]\begin{gathered} V_s=\text{Volume of the smaller pyramid} \\ V_s=27in^3 \\ V_l=\text{Volume of the larger pyramid} \\ V_l=343in^3 \end{gathered}[/tex]Define scale factor
The scale factor of two similar shapes can be defined as the ratio of the length of the initial shape to the length of the final shape.
Find the ratio of the Volume
The ratio of the volume of the smaller pyramid to the larger pyramid is
[tex]\frac{V_s}{V_l}=\frac{27}{343}[/tex]State the relationship between the volume of a pyramid to the length
The unit of measure of the volume is the cube of the length (for example if the unit of the length is inches, the unit of the volume would be cubic inches). While the unit of the length is the cube root of the unit of the volume
Find the ratio of the length
The ratio of the length would be the cube root of the ratio of the volume
[tex]\frac{l_s}{l_l}=\sqrt[3]{\frac{27}{343}}=\frac{\sqrt[3]{27}}{\sqrt[3]{343}}=\frac{3}{7}[/tex]Since the scale factor is the ratio of the length,
Hence, the scale factor is 3/7
The solutions obtained after plotting the quadratic equationy = –2x^2 + 3x-1 in the coordinate plane are ?
The solutions are:
[tex]\begin{gathered} (0.5,0) \\ and \\ (1,0) \end{gathered}[/tex]Solutions:
[tex]\begin{gathered} x=\frac{1}{2}=0.5 \\ x=1 \end{gathered}[/tex]the estimated value of 63×38
We have to estimate
[tex]63\times38[/tex]We can round them to nearest 10s.
63 would become 60
38 would become 40
So, you will be left with
60 x 40
That would be:
2400
Please help and explain i’m really slow and i’m confused.
For part a:
8 - (?) = 18
We need to find a number that subtracted from 8 gives us 18. That's number is -10, because:
8 - ( - 10) = 8 + 10 = 18
For part b:
[tex]\frac{-21}{?}=-7[/tex]We need to find a number such that -21 divided by that number is equal to -7, So, the missing number is 3, because:
[tex]\frac{-21}{3}=-7[/tex]For part c:
16 + ? = -36
We need to find a number that added to 16 give as -36. The missing number is -52, because:
16 + (- 52) = 16 - 52 = -36
For part d:
-6(?) = 66
We need to find a number that multiplies by -6 give us 66, that number is -11, because:
-6*(-11) = 66
For last part:
(?)^2=25
We need to find a number that to the power of 2 is equal to 25. The possible numbers are 5 and -5 because:
[tex]\begin{gathered} 5^2=5\cdot5=25 \\ (-5)^2=(-5)\cdot(-5)=25 \end{gathered}[/tex]Answers: a. 18
b. 3
c. -52
d. -11
e. 5 and -5
Given the polynomial functions f(x) and g(x) , find h(x) = f(x) - g(x) . f(x) = 4x ^ 4 - x ^ 3 + 3x ^ 2 + 6; g(x) = 5x ^ 3 - 2x ^ 2 + 3x - 2
Solution:
Given:
[tex]\begin{gathered} f(x)=4x^4-x^3+3x^2+6 \\ g(x)=5x^3-2x^2+3x-2 \\ h(x)=f(x)-g(x) \end{gathered}[/tex][tex]\begin{gathered} h(x)=f(x)-g(x) \\ h(x)=4x^4-x^3+3x^2+6-(5x^3-2x^2+3x-2) \\ \text{Expanding the bracket with the negative sign,} \\ h(x)=4x^4-x^3+3x^2+6-5x^3+2x^2-3x+2 \\ \text{Collecting the like terms and then simplifying further;} \\ h(x)=4x^4-x^3-5x^3+3x^2+2x^2-3x+6+2 \\ h(x)=4x^4-6x^3+5x^2-3x+8 \end{gathered}[/tex]Therefore,
[tex]h(x)=4x^4-6x^3+5x^2-3x+8[/tex]The SECOND OPTION is the correct answer.