Answer:
(7,-2)
Step-by-step explanation:
3x+2y=17
-2x-y=-12
Multiply the second equation by 2 so we can eliminate y
2( -2x-y=-12) becomes -4x-2y = -24
Add this to the first equation
3x+2y=17
-4x-2y=-24
----------------
-x = -7
Multiply each side by -1
x = 7
Substitute back into the first equation to find y
3(7) +2y = 17
21 +2y = 17
Subtract 21 from each side
21-21 +2y = 17-21
2y = -4
Divide each side by 2
2y/2 = -4/2
y =-2
(7,-2)
Answer:
x = 7, y = -2Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}3x+2y=17&(1)\\-2x-y=-12&(2)\end{array}\right\\\\(2)\\-2x-y=-12\qquad\text{add 2x to both sides}\\-y=2x-12\qquad\text{change the signs}\\y=-2x+12\qquad\text{substitute it to (1):}\\\\3x+2(-2x+12)=17\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\3x+(2)(-2x)+(2)(12)=17\\3x-4x+24=17\qquad\text{subtract 24 from both sides}\\-x=-7\qquad\text{change the signs}\\\boxed{x=7}\\\\\text{Put the value of x to (2):}\\\\y=-2(7)+12\\y=-14+12\\\boxed{y=-2}[/tex]
Elimination method
2x-7y=0
4x+9y=0
Answer:
The answer to the question
Find the sum of 14+20+26+...+1244
The sum of the series 14+20+26+...+1244 is 129,045.
The question is to find the sum of the sequence 14+20+26+...+1244. This is an arithmetic series where the common difference (d) is 6, since each term is 6 more than the previous term. The first term (a1) is 14.
To find the sum of the series, we need to determine the number of terms (n). The nth term of an arithmetic series is given by an = a1 + (n-1)d. We will set an to 1244, the last term, and solve for n:
1244 = 14 + (n-1) × 6
n = (1244 - 14)/6 + 1
n = 205
Now that we have the number of terms, we can use the sum formula for an arithmetic series which is S = n/2 × (a1 + an). Thus:
S = 205/2 × (14 + 1244)
S = 102.5 × 1258
S = 129,045
So, the sum of the series 14+20+26+...+1244 is 129,045.
find the equation of the line using the slope formula. Write the final equation using the slope-intercept form. the x- intercept is 1, and (x,y) = ( -2, 12) is a point on the line
Answer:
[tex]y=- 4x + 4[/tex]
Step-by-step explanation:
The slope formula for a straight line is:
[tex]y=mx+b[/tex]
Where, 'm' is the slope and 'b' is the y-intercept.
To find the x-intercept of a line, we need to equal 'y' to zero, and then solve for 'x'. In this case we know that the x-intercept is 1, so we have the point (x1, y1)=(1,0). We are given a second point which is: (x0, y0)=(-2, 12).
To find the slope, we use the following formula:
[tex]m = \frac{y1-y0}{x1-x0} = \frac{0-12}{1-(-2)} = -4 [/tex]
Now, The equation of the line is: y - y0 = m(x-x0). Then, substituting the values of 'm', 'x0' and 'y0' we have that:
[tex]y - 12 = -4(x+2) ⇒ y = -4x-8 + 12 ⇒ y=- 4x + 4[/tex]
The equation of the line using the slope-intercept form is:
[tex]y=- 4x + 4[/tex]
The Transitive Property of Congruence allows you to say that if ∠PQR ≅ ∠RQS, and ∠RQS ≅ ∠SQT, then _____.
1.) ∠RQS ≅ ∠PQR
2.) ∠PQR ≅ ∠SQT
3.) ∠PQR ≅ ∠RQS
4.) ∠RQS ≅ ∠RQP
The answer would be 2. Angle PQR = Angle SQT
Hope it helps :)
Answer is 2 for sure Goodluck.
The cost of renting a car is 35/we plus $0.25/mi traveled during that week. An equation to represent the cost would be y= 35+0.25x, where x is the number of miles traveled. Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?
ANSWER
260 miles
EXPLANATION
The equation that models the cost is
[tex]y = 35 + 0.25x[/tex]
If you have a maximum of $100 to spend for the car rental, then we can equation the cost function to
$100 to determine the maximum number of miles you could travel.
[tex]35 + 0.25x = 100[/tex]
[tex]0.25x = 100 - 35[/tex]
[tex]0.25x = 65[/tex]
[tex]x = \frac{65}{0.25} [/tex]
[tex]x = 260mi[/tex]
Therefore the maximum number of miles you can travel is 260 miles
which is the best name for the quadrilateral with vertices at (2,2) (5,-2) (1,-5) (-2,-1)
Answer:
square
Step-by-step explanation:
A graph reveals all side lengths are the same and sides are perpendicular. The quadrilateral is a square.
in a triangle, a 32° angle is between two sides of 6 feet and 8 feet. what is the length of the thrid side, in feet?
Answer:
4.3 feet
Step-by-step explanation:
Please I need help!!! Mr. weber ran 5 miles in 33 min. How fast can he run 26.2 miles?
Answer:
172.92 minutes
Step-by-step explanation:
Step 1: Write a proportion
33/5 = X/26.2
Step 2: Solve your proportion
X = 172.92
Find the rate for the number of minutes per mile. (# of minutes/mile)
33 minutes/5 miles = 6.6 minutes/mile
It takes him 6.6 minutes to run a mile, so you can multiply 26.2 miles by 6.6 minutes to find how long it takes him to run 26.2 miles.
26.2(6.6) = 172.92 minutes
Please help me for this homework
Answer:
None
Step-by-step explanation:
Follow me To get The Answer
Answer:
123. [tex]A=lw[/tex], [tex]A=72[/tex]
124. B) 20 square feet
125. C) [tex]\frac{1}{6}[/tex]
126. A) 24 + 12, B) (4*6)+(4*3)
127. 30, 36, 44
Step-by-step explanation:
123. Area = length*width
Substitute '9' for [tex]l[/tex] and '8' for [tex]w[/tex].
[tex]A=(9)(8)[/tex] or [tex]A=(9*8)[/tex]
[tex]9*8=72[/tex], so [tex]A=72[/tex].
124. Using the formula [tex]A=lw[/tex], substitute '5' for [tex]l[/tex] and '4' for [tex]w[/tex].
[tex]A=(5)(4)[/tex] or [tex]A=(5*4)[/tex]
[tex]5*4=20[/tex], so [tex]A=20[/tex].
125. The hexagon was divided into 6 triangles, so each of the triangles is one out of six, one sixth ([tex]\frac{1}{6}[/tex].
126. The lighter rectangle's area is 24 and the darker's is 12 because (4*6) = 24 and (4*3) = 12.
127. For these shapes, I am using the 'subtraction' method (find the area of the shape as if it were a larger rectangle, then subtract the 'blank' spaces).
A(larger rectangle) = [tex]6*7=42[/tex]
A('blank' space) = [tex]3*4=12[/tex]
A(larger rectangle - 'blank' space) = [tex]42-12=30[/tex]
A(larger rectangle) = [tex]8*7=56[/tex]
A('blank' space) = [tex]5*4=20[/tex]
A(larger rectangle - 'blank' space) = [tex]56-20=36[/tex]
A(larger rectangle) = [tex]8*6=48[/tex]
A('blank' space) = [tex]2*1=2[/tex] (there are two of them (both equal), so add them both together) 2 + 2 = 4.
A(larger rectangle - 'blank' space) = [tex]48-4=44[/tex]
PLZZ HELP BASIC ALGEBRA
Solve the equation
8+2z=3(2-z)
Answer:
z = [tex]-\frac{2}{5}[/tex] or - 0.4
Step-by-step explanation:
8+2z = 6 - 3z
2z = 6 - 8 - 3z
2z + 3z = - 2
5z = -2
z = [tex]-\frac{2}{5}[/tex] or - 0.4
what is the center of the circle given by the equation x^2+y^2-14y-15=0
Answer:
(0, 7)Step-by-step explanation:
The equation of a circle in the standard form:
[tex](a-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the equation:
[tex]x^2+y^2-12y-15=0[/tex]
Convert into a standard form using
[tex](a-b)^2=a^2-2ab+b^2\qquad(*)[/tex]
[tex]x^2+\underbrace{y^2-2(y)(7)+7^2}_{(*)}-7^2-15=0\\\\(x-0)^2+(y-7)^2-49-15=0[/tex]
[tex](x-0)^2+(y-7)^2-64=0[/tex] add 64 to both sides
[tex](x-0)^2+(y-7)^2=64[/tex]
The center (0, 7)
The radius: r = √64 = 8
Plz help me with this
Answer:
4 n - 7
Step-by-step explanation:
- 3 , 1 , 5 , 9
The difference between the terms is 4, so our multiplier is 4 n
4 , 8 , 12 , 16 ( The 4 times tables )
-3 , 1 , 5 , 9 ( The original sequence )
What are we doing to get from the 4 times tables to get to the original sequence?
4 - - 3 = 7
8 - 1 = 7
12 - 5 = 7
16 - 9 = 7
We are subtracting 7 so our complete general term is 4 n -7
Probability and Statistics
Suppose the x-axis of a density graph represents someone's height in inches. If the area under the density curve from 60 inches to 70 inches is 0.65, what is the probability of someone's height being anywhere from 60 inches to 70 inches?
A. 70%
B. 65%
C. 75%
D. 60%
Answer:
b
Step-by-step explanation:
Also got B if you it’s not right let me know send me a comment and I will try to help with the best of my ability
{(-3, 7.5) , (-2, 10) , (-1, 12.5)} arithmetic or geomatic
Answer:
arithmetic
Step-by-step explanation:
The points fall on a straight line. They won't do that for a geometric sequence.
___
Normally the terms of either sort of sequence are numbered with counting numbers: 1, 2, 3, .... Your x-values are negative, so are obviously not term numbers of a sequence. The differences of x-values are 1, and the differences of y-values are 2.5, so we know the x- and y-values are linearly related. That relationship can be expressed in point-slope form by ...
y = 2.5(x +1) +12.5
which can be simplified to
y = 2.5x +15
__
The arithmetic sequence with first term 17.5 and common difference 2.5 would be described by this same equation.
Abc is a rectangle find m angle AEB
Check the picture below.
Answer:
The correct answer is last option.
m<AEB = 140
Step-by-step explanation:
From the figure we can see rectangle.
It is given that, m<ADE = 70°
To find the value of m<AEB
From the figure we get Triangle ADE is isosceles triangle
<DAE = 70°
Therefore m<AED = 180 - (70 + 70) = 40°
<AED and <AEB are linear pairs
Therefore m<AEB = 180 - m<AED
= 180 - 40 = 140
The correct answer is last option
140
A circle is centered at N (-6 -2) The point E (-1, 1) is on the circle. Where does the point H (-10, -7) lie?
so we know the point E is on the circle, thus the distance NE is really the radius of the circle hmmm what would that be?
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad E(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[-1-(-6)]^2+[1-(-2)]^2}\implies r=\sqrt{(-1+6)^2+(1+2)^2} \\\\\\ r=\sqrt{5^2+3^2}\implies r=\sqrt{34}\implies r\approx 5.83 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad H(\stackrel{x_2}{-10}~,~\stackrel{y_2}{-7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ NH=\sqrt{[-10-(-6)]^2+[-7-(-2)]^2} \\\\\\ NH=\sqrt{(-10+6)^2+(-7+2)^2}\implies NH=\sqrt{(-4)^2+(-5)^2} \\\\\\ NH=\sqrt{41}\implies NH\approx 6.4\impliedby \begin{array}{llll} \textit{units away from the center}\\ \textit{is outside the circle} \end{array}[/tex]
recall the radius is about 5.83, anything shorter than that is inside the circle, anything longer than that is outside it.
Answer:
outside the circle
Step-by-step explanation:
trust me. i did it on khan academy
pls help math
12x+110=6(x+100)
15 points
move parentheses by 6. 12x+110=6x+600
move variable to its left side and change its term 12x+110-6x=100
collect like terms and subtract 12 the divide both sides by 6.
answer 81.666666666666
Answer:
[tex]x = 230/3\\[/tex]
Step-by-step explanation:
Step 1: Distribute
12x + 110 = 6(x + 100)
12x + 110 = (6 * x) + (6 * 100)
12x + 110 = 6x + 600
Step 2: Subtract 6x from both sides
12x + 110 - 6x = 6x + 600 - 6x
6x + 110 = 600
Step 3: Subtract 110 from both sides
6x + 110 - 110 = 600 - 110
[tex]6x = 490[/tex]
Step 4: Divide both sides by 6
[tex]6x / 6 = 490 / 6[/tex]
[tex]x = 490 / 6[/tex]
[tex]x = (460/2) / (6/2)[/tex]
[tex]x = 230/3[/tex]
Answer: [tex]x = 230/3\\[/tex]
On a map with a scale of 1 inch= 12 miles, the distance between two cities is 4
inches. What is the actual distance between the two cities?
48 miles. If 1 inch means 12 miles you can multiply both sides by 4 to get "4 inches = 48 miles"
Select the correct answer.
Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were allergic to penicillin, Nathan had a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The test is 98% accurate. What is the probability that Nathan is allergic to penicillin and the test predicts it?
Answer:
[tex]P=0.735[/tex]
Step-by-step explanation:
Call A to the event in which Nathan is allergic to penicillin
So
[tex]P (A) = 0.75[/tex]
[tex]P (A') = 1-P (A) = 0.25[/tex]
Call B the event in which the skin test predicts correctly.
So:
[tex]P (B) = 0.98\\P (B ') = 1-P (B) = 0.02[/tex]
We look for the probability that Nathan is allergic to penicillin and the test predicts it.
This is [tex]P (A\ and\ B)[/tex].
[tex]P (A\ and\ B) = P (A)*P (B)\\\\P (A\ and\ B) = 0.75 * 0.98\\\\P (A\ and\ B) = 0.735[/tex]
I need help please. Quick.
It would be A.
All of the others include “Natural Numbers” -5 is not a natural number. A natural number is a counting number like 1,2,3,4,5.
Answer: I believe your answer is A.
hope you get 100%! ^.^
Subtract (8x-2) -(5x-7)
Answer:
[tex]3x+5[/tex]
Step-by-step explanation:
we have
[tex](8x-2)-(5x-7)[/tex]
step 1
Eliminate the parenthesis
[tex](8x-2)-(5x-7)=8x-2-5x+7[/tex]
step 2
Groupe terms that contain the same variable
[tex]8x-5x-2+7[/tex]
step 3
Combine like terms
[tex]3x+5[/tex]
The simplified expression of (8x-2) -(5x-7) is said to be 3x + 5.
What is the Subtraction?To subtract the expression (8x - 2) - (5x - 7), we can use the distributive property to remove the parentheses. Here's the step-by-step solution:
(8x - 2) - (5x - 7)
Do, Remove the parentheses:
8x - 2 - 5x + 7
Combine like terms:
(8x - 5x) + (-2 + 7)
Hence:
3x + 5
Therefore, the simplified expression is 3x + 5.
Read more about Subtraction here:
https://brainly.com/question/13378503
#SPJ6
What is the volume of right rectangular prism with a height of 15 feet length of 24 inches and width of 6 feet
Answer:
2,160 [tex]ft^{3}[/tex]
Step-by-step explanation:
The formula is V = lhw
15 x 24 x 6 = V
15 x 24 = 360
360 x 6 = 2,160
2,160[tex]ft^{3}[/tex]
Answer: 180 ft³
Step-by-step explanation:
You can calculate the volume of a right rectangular prism with this formula:
[tex]V=lwh[/tex]
Where "l" is the length and "w" is the width.
You know that the height of that this right rectangular prism is 15 feet, its length is 24 inches and its width is 6 feet.
Then, you need to make the conversion from 24 inches to feet (1 feet=12 inches):
[tex]l=(24in)(\frac{1ft}{12in})= 2ft[/tex]
Then, susbtituting values, you get:
[tex]V=(2ft)(6ft)(15ft)=180ft^3[/tex]
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -3 + 3 sin θ
Answer:
y-axis
Step-by-step explanation:
find the value of 9!/(9-32)
Step-by-step explanation:
[tex]n!=1\cdot2\cdot3\cdot...\cdot n\\\\\dfrac{9!}{9-32}=\dfrac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9}{-23}=-\dfrac{362880}{23}[/tex]
elimination/subtraction
3x - 10y=-70
4x +9y = 63
(can you please explain in step by step?)
Answer:
x = 0, y = 7
Step-by-step explanation:
Solving a system of equations using substitution requires one side to be equal to a variable present in the equation, in this case x or y. We should simplify the equation using elimination before substituting to reduce the chance of error.
In order to use the elimination method, you have to create variables that have the same coefficient—then you can eliminate them. These equations arew already aligned for us.
3x - 10y=-70
- 4x +9y = 63
-x + y = 7
Now, for substitution, the equation must be set to a variable.
-x + y = 7
y = x + 7
Next, plug the equation in where applicable in another equation.
4x +9(x + 7) = 63
4x + 9x + 63 = 63
13x = 0
x = 0
The final step of substitution is to plug the known variable into an equation to find the other variable.
3(0) - 10y=-70
0 - 10y = -70
10y = 70
y = 7
I guarantee you this answer is correct, I worked it out using other methods and graphing prior to submitting this answer.
Answer:
x = 0 , y = 7
Step-by-step explanation:
[tex]3x - 10y = - 70..............(1) \\ 4x + 9y = 63...................(2) \\ (1) \times 4 \\ 12x - 40y = - 280...........(3) \\ (2) \times 3 \\ 12x + 27y = 189...........(4) \\ (4) - (3) \\ 67y = 469 \\ \\ y = \frac{469}{67} \\ y = 7 \\ put \: y = 7 \: into \: (1) \\ 3x - 10(7) = - 70 \\ 3x - 70 = - 70 \\ 3x = - 70 + 70 \\ 3x = 0 \\ x = \frac{0}{3} \\ x = 0[/tex]
find the value of k for which one root of the quadratic equation kx2 14x 8 = 0 is 6 times the other
Answer:
k = 3.
Step-by-step explanation:
If the 2 roots are A and B we have the relations:
AB = 8/k and A+B = -14/k.
We are given that A = 6B so
6B^2 = 8/k
B^2 = 8/6k = 4/3k
B = 2 /√(3k) ......(1)
Now A + B = -14/k so
6B + B = 7B = -14/k
B = -2/k..........(2)
Eliminating B from equations (1) and (2):
2 /√(3k) = -2/k
Cross multiply:
2k = -2√(3k)
Squaring both sides:
4k^2 = 4 * 3k
4k^2 = 12k
k^2 = 3k
k = 3.
To find the value of k, we first define the roots as p and 6p. We then use the properties of the sum and product of roots in a quadratic equation to form two equations. We can solve these equations to get the value of k.
Explanation:The given quadratic equation is kx2 + 14x + 8 = 0. We are looking for the value of k for which one root of the equation is six times the other. Let's denote the roots by p and 6p (since one is 6 times the other).
For a quadratic equation ax2 + bx + c = 0, the sum of the roots is given by -b/a and the product of the roots is c/a. In this case, -b/a or -14/k is equal to the sum of the roots (p + 6p). The product of the roots, c/a or 8/k, is equal to p*6p.
From the sum of the roots equation, we can determine p = -14/7k and by substitifying p in the other equation we can solve for k.
Learn more about Quadratic Equations here:https://brainly.com/question/34196754
Convert 32 ounces to pounds
Answer: 2 pounds
Step-by-step explanation: There are 16 ounces in one pound. So when you divide 32 by 16, you get 2. Therefore your answer would be 2 pounds!
For this case we must make a conversion.
We know, by definition, that 1 ounce is equivalent to 0.0625 pounds.
We make a rule of three to determine how many pounds are 32 ounces.
1oz ---------------> 0.0625lb
32oz -------------> x
DOnde "x" represents the number of pounds
[tex]x = \frac {32 * 0.0625} {1}\\x = 2[/tex]
So, 32 ounces equals 2 pounds
Answer:
2 pounds
Which of the following is least able to transfer electrons?
Option D. an isulator
Is the right answer i guess...
As The transfer of electrons increases The cunductivity also increases...
Hope it helps...
Regards,
Leukonov/Olegion.
Answer:
Insulator
Step-by-step explanation:
As insulators are meant to prevent the conduction of electricity.
Write a function describing the relationship of the given variables.
A
varies directly with the square root of
r
and when
r
=
16
,
A
=
40
A
=
Answer:
The function is A = 10√r
Step-by-step explanation:
* Lets explain the meaning of direct variation
- The direct variation is a mathematical relationship between two
variables that can be expressed by an equation in which one
variable is equal to a constant times the other
- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the
constant of variation
* Now lets solve the problem
# A is varies directly with the square root of r
- Change the statement above to a mathematical relation
∴ A ∝ √r
- Chang the relation to a function by using a constant k
∴ A = k√r
- To find the value of the constant of variation k substitute A and r
by the given values
∵ r = 16 when A = 40
∵ A = k√r
∴ 40 = k√16 ⇒ simplify the square root
∴ 40 = 4k ⇒ divide both sides by 4 to find the value of k
∴ 10 = k
- The value of the constant of variation is 10
∴ The function describing the relationship of A and r is A = 10√r
Answer:
A = 10[tex]\sqrt{r}[/tex]
Step-by-step explanation:
Given A varies directly with the square root of r then the equation relating them is
A = k[tex]\sqrt{r}[/tex] ← k is the constant of variation
To find k use the condition r = 16 , A = 40
k = [tex]\frac{A}{\sqrt{r} }[/tex] = [tex]\frac{40}{\sqrt{16} }[/tex] = [tex]\frac{40}{4}[/tex] = 10
A = 10[tex]\sqrt{r}[/tex] ← equation of variation
Note: Enter your answer and show all the steps that you use
to solve this problem in the space provided.
A radio signal travels at 3.00 · 100 meters per second.
How many seconds will it take for a radio signal to travel from
a satellite to the surface of Earth if the satellite is orbiting at a
height of 3.54 · 10' meters? Show your work.
لیا
Answer:
O.118 seconds will be taken for a radio signal to travel from a satellite to the surface of earth.
Step-by-step explanation:
We are given Speed = 3.00 · 10^8 meters per second.
And Distance = 3.54.10^7 metwers
We need to find time.
We know that,
Distance = Speed * Time
3.54.10^7 = 3.00 · 10^8 * Time
Time = 3.54.10^7 / 3.00 · 10^8
Time = 1.18 X 10^7-8
Time = 1.18 x 10^-1
Time = 0.118 seconds.
So, O.118 seconds will be taken for a radio signal to travel from a satellite to the surface of earth.