We have to find the solution for this equations.
a) -30 = -10(q-1)
[tex]\begin{gathered} -30=-10(q-1) \\ q-1=\frac{-30}{-10} \\ q-1=3 \\ q=3+1 \\ q=4 \end{gathered}[/tex]b) 6+(c+8) = 13
[tex]\begin{gathered} 6+(c+8)=13 \\ c=13-6-8 \\ c=-1 \end{gathered}[/tex]c) 6-(c+8)=13
[tex]\begin{gathered} 6-(c+8)=13 \\ 6-13=c+8 \\ -7=c+8 \\ -7-8=c \\ c=-15 \end{gathered}[/tex]d) -(c-4)=13
[tex]\begin{gathered} -(c-4)=13 \\ c-4=-13 \\ c=-13+4 \\ c=-9 \end{gathered}[/tex]f) -36= -3(2-5m)
[tex]\begin{gathered} -36=-3(2-5m) \\ \frac{-36}{-3}=2-5m \\ 12=2-5m \\ 5m=2-12 \\ 5m=-10 \\ m=\frac{-10}{5} \\ m=-2 \end{gathered}[/tex]g) 4-10(n+4)=-56
[tex]\begin{gathered} 4-10\mleft(n+4\mright)=-56 \\ 4+56=10(n+4) \\ 60=10(n+4) \\ \frac{60}{10}=n+4 \\ 6=n+4 \\ n=6-4 \\ n=2 \end{gathered}[/tex]Triangle ABC has coordinates A(-6,2), B(-3,6), and C(5,0). Find the perimeter of the triangle. Express your answer in simplest radical form.
we must know the measure of each side, for this we must calculate the distance between points
the formula is
[tex]d=\sqrt[]{(x1-x2)^2+(y1-y2)^2}[/tex]AB
[tex]\begin{gathered} \sqrt[]{(-6-(-3))^2+(2-6)^2} \\ \sqrt[]{25} \\ AB=5 \end{gathered}[/tex]AC
[tex]\begin{gathered} \sqrt[]{(-6-5)^2+(2-0)^2} \\ \sqrt[]{125} \\ AC=5\sqrt[]{5} \end{gathered}[/tex]BC
[tex]\begin{gathered} \sqrt[]{(-3-5)^2+(6-0)^2} \\ \\ \sqrt[]{100} \\ BC=10 \end{gathered}[/tex]now add all sides to find the perimeter
[tex]\begin{gathered} 5+5\sqrt[]{5}+10 \\ \end{gathered}[/tex]the perimeter is
[tex]15+5\sqrt[]{5}\approx26.18[/tex]Counting in bases less than ten
Answer:
Step-by-step explanation:
84649347
Which should figure could be formed from the net shown?
Answer
The solid figure that could be formed from the net show is a square pyramid
Explanation
The figure shown has been opened from the vertex, v, when closed, a square base of side 5 in with perpendicular height 7 in is formed. Hence, the solid figure that could be formed from the net shown is a Square pyramid
Thursday: Word Problems 1 The plant growth is proportional to time. When Tia bought the plant, it measured 2 cm. It measured 2.5 cm exactly one week later. If the plant continues to grow at this rate, determine the function that represents the plant's growth.
We have the next informtion
initial measure = 2 cm
after
What is the sum of the first 19 terms of the sequence 9,2,-5,-12....2SEE ANSWERS
ANSWER
-1026
EXPLANATION
The sum of the first n terms in an arithmetic sequence is,
[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex]As we can see, we have to find the nth term of the sequence,
[tex]a_n=a_1+(n-1)d[/tex]In this case, the first term is 9 and the common difference is -7 - note that each term is the previous one minus 7. So the formula for the nth term is,
[tex]a_n=9-7(n-1)[/tex]We have to find the 19th term,
[tex]a_{19}=9-7(19-1)=9-7\cdot18=9-126=-117[/tex]So the sum of the first 19 terms is,
[tex]S_{19}=\frac{19\cdot(9+(-117))}{2}=\frac{19\cdot(9-117)}{2}=\frac{19\cdot(-108)}{2}=\frac{-2052}{2}=-1026[/tex]Hence, the sum of the first 19 terms of the given sequence is -1026.
Writing an equation of an… Given the foci and major axis length
We need to find the equation of the ellipse given the foci and major axis.
The equation is given by:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]We have the foci points at (2,4) and (2,-6). The distance is 10 units, then the center is equal to half value c=5.
If the length of the major axis is 12.
Major axis length = 2a
Then
12 = 2a
a=12/2
a=6
To find b, we have the next equation:
[tex]\begin{gathered} b^2=a^2-c^2 \\ Replacing \\ b^2=6^2-5^2 \\ b^2=36-25 \\ b^2=11 \\ Solve\text{ for b} \\ b=\sqrt[]{11} \end{gathered}[/tex]Now, the center c is given by the point (2,-1). This point is in the middle of both foci points
Finally, we can replace on the ellipse equation:
[tex]\begin{gathered} \frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1 \\ Replacing,\text{ the result is} \\ \frac{(x-2)^2}{6^2}+\frac{(y-(-1))^2}{(\sqrt[]{11})^2}=1 \end{gathered}[/tex]Two investments are made summing up to 8,800. For a certain year, theseinvestments yield P1,326 in simple interest. Part of the investment is allotted for14% and part for 16%. Find the amount invested at each rate
Given:
a.) Two investments are made summing up to 8,800.
b.) For a certain year, these investments yield P1,326 in simple interest.
c.) Part of the investment is allotted for 14% and part for 16%.
Recall: The simple interest formula.
[tex]\text{ I = Prt}[/tex]Where,
I = interest
P = principal amount
r = interest rate
t = time (in year)
Step 1:
P = 8,800
But it's been made into two investments.
Let,
A = investment 1
B = investment 2
We get,
A + B = 8,800 = P (Equation 1)
Step 2:
Part of the investment is allotted for 14% and part for 16%.
Thus,
For investment 1:
Ia = Art = A(14/100)(1) = 0.14A
For investment 2:
Ib = Brt = B(16/100)(1) = 0.16B
We get,
0.14A + 0.16B = 1,326 (Equation 2)
Step 3:
Substitute Equation 1 to Equation 2.
A + B = 8,800
A = 8,800 - B
0.14A + 0.16B = 1,326
0.14(8,800 - B) + 0.16B = 1,326
1,232 - 0.14B + 0.16B = 1,326
0.02B = 1,326 - 1,232
0.02B = 94
0.02B/0.02 = 94/0.02
B = 4,700
Let's now find A.
A + B = 8,800
A + 4,700 = 8,800
A = 8,800 - 4,700
A = 4,100
In Summary:
The amount invested at 14% is 4,100
The amount invested at 16% is 4,700
l will send u the pic
as they are in the same line, the measures of angles AOD and angle DOC they measure 180°
find the length between the big circle and small circle.
First, we will calculate the hypotenuse of the first triangle
[tex]\begin{gathered} \cos 51=\frac{11}{h} \\ h=\frac{11}{\cos51} \\ h=17.48 \\ \end{gathered}[/tex]Now let's calculate the angle a
[tex]\begin{gathered} a=180-64-54 \\ a=65 \end{gathered}[/tex]Total result
T = 17.48+12.204+2.62+4.72
T = 37.024
The answer would be 37.024
for all triangles input data entered: side a, b and angle γ.
Calculation of the third side c of the triangle using a Law of Cosines
[tex]c^2=a^2+b^2-2ab\cos \gamma[/tex]The probability that it is Tuesday and Robert is absent is 0.04.There are 5 school working days in a week and the probabilitythat it is Tuesday is 0.5. What is the probability that Robert isabsent given that today is Tuesday?
The probability is 8%.
From the question, we have
The probability that it is Tuesday and Robert is absent is 0.04.
P(Tuesday and absent) = 0.04
P(Tuesday) =0.5
P(absent/Tuesday) =0.04/0.5 = 0.08
=0.08*100%
=8%
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Suppose f(x)=5x+6 . Describe how the graph of g compares with the graph of f . g(x)=f(x+5)
g(x) = f(x) + 5 relates to f(x) by shifting f(x) 5 units up.
What is a function?The link between two independent variables and one dependent variable is described by a mathematical expression, rule, or law (the dependent variable).
An example of a rule is a function, which produces one output for a single input. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. We can infer that y is a function of x because x is the input value.
The function is given as:
f(x) = 5x+6
g(x) = f(x)+5
this gives,
g(x) = 5x+6+5
g(x) = 5x+11
g(x) = f(x) + 5 relates to f(x) by shifting f(x) 5 units up.
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6:4= :2 I dont know what that is
Answer: x = 3
Let the missing number be x
6 : 4 = x : 2
ratio is the same as fraction
6/4 = x/2
Step2 : cross multiply
x * 4 = 6 * 2
4x = 12
Divide both sides by 4
4x/4 = 12/4
x = 3
Therefore, the missing number is 3
What is the volume of the prism shown by the net?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
length = 1/2 yd
width = 1/4 yd
height = 1/6 yd
Volume = ?
Step 02:
Volume = l * w * h
[tex]V\text{ = }\frac{1}{2}yd\cdot\frac{1}{4}yd\cdot\frac{1}{6}yd=\frac{1}{48}yd^3[/tex]The answer is:
The volume of the right rectangular prism is 1 / 48 yd³ .
i only need help with question 3 thats in the attachment
Answer:
Step-by-step explanation:
3) Parallel and equal
b/c the sides are parallel, and also, b/c there is a right angle in the interior, it makes the sides equal length also.
I need help please Question 9 Help for my homework
Given the figure of a triangular prism.
We will find the amount of wood to make the wooden play block
So, we will find the volume of the given block
As shown: the triangular side has a base of 4 cm and a height of 6 cm
The area of the triangular base =
[tex]\frac{1}{2}*4*6=12\text{ }cm^2[/tex]the length between the triangular sides = 12 cm
So, the volume = base area * length =
[tex]12*12=144\text{ }cm^3[/tex]So, the answer will be the first option 144 cm³
Hannah reads at a constant rate of 3 pages every 8 minutes. Write an equation that shows the relationship between p, the number of pages she reads, and m, the number of minutes she spends reading. Report a probler
Since we have that Hannah reads 3 pages every 8 minutes, we will construct the function by first knowing how many pages she reads in 1 minute, that is:
She reads 3/8 pages each minute, then we will construct the function as follows:
[tex]p=\frac{3}{8}m[/tex]Where p is the number of pages and m is the number of minutes that she reads. We can see that this describes is if we solve for 1 minute and 8 minutes. If we solve for 1 minute, we get she read 3/8 pages and if we replace 8 minutes, we will get that she reads 3 pages.
A garage has 60 vehicles for sale, which
are all either new or second-hand.
28 of the vehicles are cars and the rest are
vans.
Of the cars, 7 are second-hand.
5 of the vans are new.
a) By copying and completing the
frequency tree below to show this
information, work out the value that should
replace D in the frequency tree.
b) In total, how many of the vehicles are
second-hand?
The number of vehicles that are secondhand is 34.
There is a garage. The total number of vehicles in the garage is 60. The vehicles are for sale. The vehicles are all either new or secondhand. The number of vehicles that are cars is 28. The other vehicles are vans. Seven of the cars are secondhand. Five of the vans are new. We have to find the total number of second-hand vehicles.
First of all, we will find the number of vans in the garage. The number of vans is 60 - 28 = 32. The number of cars that are second-hand is 7. The number of vans that are second-hand is 32 - 5 = 27.
The total number of second-hand vehicles in the garage is the sum of the numbers of second-hand cars and vans.
N = 7 + 27
N = 34
Hence, 34 vehicles are second-hand in the garage.
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Is the LCD Going to be 5 • 7 •z = 35 ?
To add these fractions, we can do the following steps.
Step 1: Simplify each fraction.
[tex]\frac{25}{5y}=\frac{5\cdot5}{5y}=\frac{5}{y}[/tex][tex]\frac{64}{8y}=\frac{8\cdot8}{8y}=\frac{8}{y}[/tex]Step 2: We add the numerators since the fractions have the same denominator.
[tex]\frac{5}{y}+\frac{8}{y}=\frac{5+8}{y}=\frac{13}{y}[/tex]Therefore, the result of adding the fractions is 13/y.
Re-write the equation in slope-intercept form: 3x - 2y =6
To write it in the slope intercept form we have to slove the equation to y:
[tex]\begin{gathered} 3x-2y=6\rightarrow \\ 2y=3x-6 \\ y=\frac{3}{2}x-3 \end{gathered}[/tex]Find the area of this irregular shape.
[Round off to the nearest whole number.]
sq. units
Answer:
grubby me and I will be there in a few minutes to talk to you about it do you
nose
Step-by-step explanation:
nosediving the Gigi Hadid and wirt me and wirt me and I will be there in a few minutes to talk to you about it
Question Solve: s + 159 = 25.
We have to solve for s:
[tex]\begin{gathered} s+159=25 \\ s+159-159=25-159 \\ s=-134 \end{gathered}[/tex]Answer: s = -134
In a direct variation, y = -18 when x = -3. Write a direct variation equation that shows therelationship between x and y.Write your answer as an equation with y first, followed by an equals sign.Submit
The direct variation between y and x has the following
3. A savings account is started with an initial deposit of $1500.The account earns 1.8% interest compounded annually.(a) Write an equation to represent the amount of money inthe account as a function of time in years. 5 Points(B) how much more interest would be earned if the initial deposit is allowed to earn interest for 20 years vs 10 years
a) We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
where
A = the total amount in the account at the end of t years
r = interest rate
n = the periodic interval at which it was compounded
P = the principal or initial amount deposited
From the information given,
P = 1500
r = 1.8/100 = 0.018
n = 1 because it is compounded once in a year
Thus, an equation to represent the amount of money in the account as a function of time in years ia
A = 1500(1 + 0.018/1)^1 * t
A = 1500(1.018)^t
B) If t = 20, then
A = 1500(1.018)^20
A = 2143.12
The interest earned would be the total amount - the principal
Interest earned after 20 years = 2143.12 - 1500 = 643.12
If t = 10, then
A = 1500(1.018)^10
A = 1792.95
Interest earned after 10 years = 1792.95 - 1500 = 292.95
Thus, the difference in interest earned between both years is
643.12 - 292.95
= $350.17
Write the function in factored form.
y = -2x³-4x²+4x+30x
I need help :)
The factored form is y = 2x(−x²−2x+17).
From the question, we have
y = -2x³-4x²+4x+30x
=−2x³−4x³+4x+30x
=−2x³−4x³+34x
=2x(−x²−2x+17)
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of sines, what is the measure of side a? Round your answer to the nearest whole number, if necessary.c = 9 cmA = 22°C = 13°Answers24 cm40 cm5 cm15 cm
Given
There is a triangle with sides a, b, and c and angles A, B, and C.
And,
c = 9 cm
A = 22°
C = 13°
To find:
The value of a.
Explanation:
It is given that,
There is a triangle with sides a, b, and c and angles A, B, and C.
And,
c = 9 cm
A = 22°
C = 13°
That implies,
By using sine law,
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \Rightarrow\frac{\sin13\degree}{9}=\frac{\sin22\degree}{a} \\ \Rightarrow a=\frac{9\times\sin22\degree}{\sin13\degree} \\ \Rightarrow a=14.9875 \\ \Rightarrow a=15cm \end{gathered}[/tex]Hence, the value of a is 15cm.
Which of the following equations are equivalent (i.e. have the same solution for x)? Check all that apply.A X+1=4B 9+X=6C -5+x=-2D 2+x=5E X+(-4)=7
Solve the following equations and find those that have the same solution for x.
A
x + 1 = 4
Subtracting 1:
x = 3
B
9 + x = 6
Subtracting 9:
x = -3
C
-5 + x = -2
Adding 5:
x = 3
D
2 + x = 5
Subtracting 2:
x = 3
E
x + (-4) = 7
Operating:
x - 4 = 7
Adding 4:
x = 11
Only equations A, C, and D are equivalent
Find the range of the function.f(x) = (x + 5)^2 + 8possible ans: y > - 8y ≥ 8y > 8All real numbers
SOLUTION
Given:
Explanation:
The range is the set of possible output values, which are shown on the y -axis.
The graph of the function will help us to find range.
Looking at the graph, the y values are from 8 up to infinity.
Final answer:
The scatter plot and line of best fit below show the length of 12 people's femur (thelong leg bone in the thigh) and their height in centimeters. Based on the line of besfit, what would be the predicted height for someone with a femur length of 72 cm?Answer: ____ cm.
Answer:
230
Explanation:
First, we find the equation fo the line point-slope form.
The slope of the line is
[tex]m=\frac{209-202}{63-60}=\frac{7}{3}[/tex]With the slope of the line in hand, we now write the point-slope form of the equation using the point (63, 209)
[tex]y-209=\frac{7}{3}(x-63)[/tex]With the equation of the line in hand, we now use it to find the value of y at x = 72.
Putting in x = 72 in the above equation gives
[tex]y-209=\frac{7}{3}(72-63)[/tex][tex]y-209=\frac{7}{3}\cdot9[/tex][tex]y-209=21[/tex]adding 209 to both sides gives
[tex]y=230[/tex]which is our answer!
Hence, the predicted height for someone with a femur length of 72 cm is 230 cm.
12) Alyssa draws a rectangle that is 2/3 of ameter long and 3/5 of a meter wide. What isthe area of this rectangle?
A=LW
L=2/3
W=3/5
A= (2/3)(3/5)
A=2/5 or 0.4
let f(x) = 10x-10. Find the value of (f o f^-1) (-10)a)0b)1c)10d)-10
Solution
We are given the following expression to evaluate:
[tex]\begin{gathered} f(x)=10x-10 \\ \\ \text{ Find:} \\ (f\mathrm{}f^{-1})(-10) \end{gathered}[/tex]- In order to solve this question, we should apply the following theorem:
[tex]f(f^{-1})(x)=x_{}[/tex]- Thus, in order to solve the question, we simply substitute x = -10. This is done below:
[tex]\begin{gathered} f(f^{-1})(x)=x \\ \text{put }x=-10 \\ \\ f(f^{-1})(-10)=-10\text{ (OPTION D)} \end{gathered}[/tex]Final Answer
The answer is:
[tex]f(f^{-1})(-10)=-10\text{ (OPTION D)}[/tex]