let's multiply both sides in each equation by the LCD of all fractions in it, thus doing away with the denominator.
[tex]\begin{cases} \cfrac{1}{2}x+\cfrac{1}{3}y&=7\\\\ \cfrac{1}{4}x+\cfrac{2}{3}y&=6 \end{cases}\implies \begin{cases} \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( \cfrac{1}{2}x+\cfrac{1}{3}y \right)=6(7)}\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{4}x+\cfrac{2}{3}y\right)=12(6)} \end{cases}\implies \begin{cases} 3x+2y=42\\ 3x+8y=72 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{using elimination}}{ \begin{array}{llll} 3x+2y=42&\times -1\implies &\begin{matrix} -3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-2y=&-42\\ 3x+8y-72 &&~~\begin{matrix} 3x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+8y=&72\\ \cline{3-4}\\ &&~\hfill 6y=&30 \end{array}} \\\\\\ y=\cfrac{30}{6}\implies \blacktriangleright y=5 \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{substituting \underline{y} on the 1st equation}~\hfill }{3x+2(5)=42\implies 3x+10=42}\implies 3x=32 \\\\\\ x=\cfrac{32}{3}\implies \blacktriangleright x=10\frac{2}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(10\frac{2}{3}~~,~~5 \right)~\hfill[/tex]
A line is drawn through (–7, 11) and (8, –9). The equation y – 11=-4/3 (x + 7) is written to represent the line. Which equations also represent the line? Check all that apply.
Answer:
[tex]y=-\frac{4}{3}x+\frac{5}{3}[/tex]
[tex]4x+3y=5[/tex]
Step-by-step explanation:
we have
[tex]y-11=-\frac{4}{3}(x+7)[/tex] -----> equation of the line into point slope form
step 1
Find the equation of the line into slope intercept form
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept (value of y when the value of x is equal to zero)
For x=0
[tex]y-11=-\frac{4}{3}(0+7)[/tex]
[tex]y=-\frac{28}{3}+11[/tex]
[tex]y=\frac{5}{3}[/tex]
therefore
[tex]b=\frac{5}{3}[/tex]
substitute
[tex]y=-\frac{4}{3}x+\frac{5}{3}[/tex] ----> equation of the line into slope intercept form
step 2
Find the equation of the line in standard form
[tex]Ax+By=C[/tex]
we have
[tex]y=-\frac{4}{3}x+\frac{5}{3}[/tex]
Multiply by 3 both sides
[tex]3y=-4x+5[/tex]
[tex]4x+3y=5[/tex] ---> equation of the line in standard form
Please answer this question correctly for 25 points and brainliest!!
Answer:
35°
Step-by-step explanation:
The measure of an inscribed angle is half the measure of the subtended arc.
x = 70°/2 = 35°
BRAINLIEST
write the algebraic expression
"the sum of 22 and four times a number"
The answer would be:
Let n be "a number"
22 + 4n
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
22+4x
Step-by-step explanation:
The number should be x as a letter symbol.
The sum should be add sign.
22+4x is the correct answer.
I hope this helps you, and have a wonderful day!
The steamboat makes the trips in 5 hours. The yacht makes the boat in 2.5 hours. The yacht is 20 knots faster than the steamboat, the trip time multiplied by the speed equals the distance traveled. You know both boats will travel the same distance. How fast is each boat traveling in knots (nautical miles per hour)?
Answer:
Steam boat = 20 Knots , Yacht = 40 Knots
Step-by-step explanation:
Let the distance travelled by both the boats be x
Case 1: Steamboat
Speed [tex]S_{s}=\frac{x}{5}[/tex]
Case 2 : Yacht
[tex]S_{y}=\frac{x}{2.5}[/tex]
[tex]S_{y}=\frac{2x}{5}[/tex]
Also given that speed of yacht is 20 more than that of steamboat
[tex]S_{y} -S_{s}=20[/tex]
Hence
[tex]\frac{2x}{5} - \frac{x}{5} = 20[/tex]
[tex]\frac{x}{5} = 20[/tex]
[tex]x = 100[/tex]
Hence the distance traveled is 100 naut miles
Hence
Speed of Steam boat = [tex]\frac{100}{5}[/tex] = 20 Knots
Speed of Yacht = [tex]\frac{100}{2.50}[/tex] = 40 Knots
how many times greater is the value of the digit 8 in 82.77 than the value of the digit 8 in 20.18
answers
1. 10 times
2. 100 times
3. 1,000 times
4. 10,000 times
if you know the answer plz answer fast I am timed on this test
Answer:
Option 3. 1,000 times
Step-by-step explanation:
we know that
The value of digit 8 in 82.77 is equal to 80
The value of digit 8 in 20.18 is 0.08
so
Divide 80 by 0.08
80/0.08=1,000 times
The value of the digit 8 in 82.77 is greater than and the value of the digit 8 in 20.18 by 1000.
The value of each digit in 82.77 is:
8 = tens
2 = units
7 = tenth
7 = hundredth
The value of each digit in 20.18 is:
2 = tens
0 = units
1 = tenth
8 = hundredth
The value of 8 in 82.77 is tens(10) and the value of 8 in 20.18 is hundredth (0.01).
Difference in value = 10 / 0.01 = 1000
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The number if marbles of different colors stored in a hat is listed below: 4 red marbles 10 green marbles 7 blue marbles. Without looking in the hat, dan takes out a marble at random. He replaces the marble and then takes out another marble from the hat. What is the probability that dan takes out a blue marble in both draws?
Answer:
1/9
Step-by-step explanation:
There are a total of 21 marbles. In the first draw, there are 7 blue marbles out of 21. In the second draw, since he replaces the marble, there are still 7 blue marbles out of 21. So the probability is:
P = (7/21)²
P = 1/9
16. Peter works part time for 3 hours every day and Cindy works part time for 2 hours every day.
a. If both of them get $4.50 an hour, write an inequality to compare Peter’s and Cindy’s earnings.
b. What should Cindy’s per-hour income be so that she earns at least $14 a day? Write an inequality and an explanation of how to solve it.
Answer:
Part A)
4.50 × 3 > 4.50 × 213.5 0 > 9Part B)
r ≥ 7Explanation:
1) The earnings are calculated multiplying the number of hours by the hourly rate.
2) The hourly rate of both Peter and Cindy is the same: $ 4.50 / hour
3) Let the variable used for computing the number of hours be h.
4) The number of hours Peter works every day is 3 hours, so, using the letter P to name Peter's earnings, the expression to calculate his earnings is:
P = 4.50 × 35) Similarly, the expression to calculate Cindy's earnings would be:
C = 4.50 × 2Answering part A)
You have to write an inequality to compare Peter's and Cindy's earnings:
4.50 × 3 > 4.50 × 213.5 0 > 9This is, the earnings of Peter are greater than the earnings of Cindy.
Part B),
You have to write an inequality to calculate Cindy's per-hour income so that she earns at least $ 14 a day.
Here, C ≥ 14, because the sign ≥ means greater than or equal to, meaning the the earnings are greater than or equal to 14.Thus, since she works 2 hours per day, the inequality becomes 2 × r ≥ $ 14, where r is the per-hour income.To solve it follow these steps:Given: 2r ≥ 14
Divide both sides by 2: r ≥ 14 / 2
Simplify: r ≥ 7
That means that Cindy's per-hour income should be at least $7 and hour so that she earns $14 a day.
what is the measure of PRQ
The angle of intersecting chords is found by adding the two arcs intercepted by the angle and dividing that by 2.
PRQ = (102 + 70) / 2
PRQ = 172 /2
PRQ = 86 degrees.
When two chords cross within a circle, the angle created is one-half the total of the arcs intercepted by the angle and its vertical angle. The measure of ∠PRQ is 86°.
What is the Angles of Intersecting Chords Theorem?When two chords cross within a circle, the angle created is one-half the total of the arcs intercepted by the angle and its vertical angle.
The measure of ∠PRQ is,
∠PRQ = (102°+70°)/2
∠PRQ = 172° / 2
∠PRQ = 86°
Hence, the measure of ∠PRQ is 86°.
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Grading Scale 2 has the following weights- Tests- 60% Quiz- 15% Homework- 10% Final Exam- 15% What do you need to score on the Final Exam to make an 78 in the class if your grades are- Show steps. Test Grades- 85 Quiz- 87 Homework- 68 Final Exam- ??
a. 85(60) + 87(15) + 68(10) + X(15) = 78 X = 49.33
b. 85(6.0) + 87(1.5) + 68(1.0) + X(1.5) = 78 X = 53.62
c. 85(.60) + 87(.15) + 68(.10) + X(.15) = 78 X = 47.67
d. 85(.60) + 87(1.5) + 68(.10) + X(1.5) = 78 X = 35.59
Answer:
c. 85(.60) + 87(.15) + 68(.10) + X(.15) = 78; X = 47.67
Step-by-step explanation:
The weighted average is the sum of products of score and weight. Choice C has the percentage weights properly expressed as decimal values.
___
The other equations could work if the final score of 78 were weighted by the corresponding equivalent of 100%. (X is wrong in the other choices as well.)
__
The attachment shows the "work". Given that choice C is the only correct equation, we presumed that the value of X was correct. The equation solver confirms this. If you want to do it by hand, compute the sum of products, subtract that sum, then divide by 0.15.
X = (78 -70.85)/.15 = 7.15/.15 = 47 2/3
In the diagram of triangle LMN, which term describes point P?
Answer:
C. Circumcenter
Step-by-step explanation:
Definitions:
Orthocenter is the point where the three "altitudes" of a triangle meet. An "altitude" is a line that goes through a vertex and is at right angles to the opposite side.
Incenter is the center of an inscribed circle (the circle that fits perfectly inside triangle, just touching all sides). It is where the "angle bisectors" (lines that split each angle in half) meet.
Circumcenter is the center of circumscribed circle. It is where the "perpendicular bisectors" (lines that are at right angles to the midpoint of each side) meet.
Centroid (or center of mass) of a triangle is the point where the three medians of the triangle meet.
As you can see from the definitions, point P is circumcenter, because it is the point of perpendicular bisectors intersection.
What is the simplest form of the expression below?
[tex]\frac{x^2yz}{y^2}[/tex]×[tex]\frac{y}{2x}[/tex]
A. [tex]\frac{xz}{2}[/tex]
B. [tex]\frac{2x^3z}{y^2}[/tex]
C. [tex]\frac{x^2z}{2y^2x}[/tex]
D. z
Answer:
[tex]\text{A.}\quad\dfrac{xz}{2}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2yz}{y^2}\times\dfrac{y}{2x}=\dfrac{x^2yzy}{2xy^2}=\dfrac{1}{2}\cdot\dfrac{x^2}{x}\cdot\dfrac{y^2}{y^2}\cdot\dfrac{z}{1}\\\\=\dfrac{xz}{2}[/tex]
How do I find the length of the sides of a right triangle?
Answer:
A^2+B^2=C^2
Step-by-step explanation:
(A)^2+(B)^2+(A)+(B)+2Cos(a)=C^2
Answer:
with a ruler?
what is the value of negative 1/2 to the fourth power?
A. -16
B. -1/16
C. 1/16
D. 16
Answer: C) 1/16
-1/2 • -1/2 • -1/2 • -1/2 =1/16
[tex]\left(-\dfrac{1}{2}\right)^{-4}=\left(-2\right)^{4}=16[/tex]
How to find the distance between two points
Answer:
Use the distance formula:
d = sqrt. ( y2 - y1)^2 + (x2 - x1)^2)
Please mark me brainliest :D Thanks!!
NEED HELP WITH A MATH QUESTION
Answer:
[tex]x = 20\°[/tex]
Step-by-step explanation:
By definition we know that the sum of the internal angles of a triangle is always equal to 180 °
in this case we have a right triangle. We know that right triangles have an angle of 90 °.
So the sum of the three sides of this triangle must be equal to 180 °
So
[tex]2x + 10 + 2x + 90 = 180[/tex]
We solve the equation for the variable x.
[tex]4x +100 = 180\\4x = 180-100\\4x = 80[/tex]
[tex]x = 20\°[/tex]
Answer: x=20
Step-by-step explanation:
2x+10+2x+90=180
4x+100=180
4x=80
X=20
Can anyone help me with this?
Reduce the fraction
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{-20t^5u^2v^3}{48t^7u^4v}\implies \cfrac{-20}{48}\cdot \cfrac{t^5u^2v^3}{t^7u^4v^1}\implies \cfrac{-5}{12}\cdot \cfrac{v^3v^{-1}}{t^7t^{-5}u^4u^{-2}}\implies \cfrac{-5}{12}\cdot \cfrac{v^{3-1}}{t^{7-5}u^{4-2}} \\\\\\ \cfrac{-5}{12}\cdot \cfrac{v^2}{t^2u^2}\implies \cfrac{-5v^2}{12t^2 u^2}[/tex]
A direct variation function contains the points( -8,-6) and (12,9). Which equation represents the function ?
Answer:
y = (3/4)x
Step-by-step explanation:
1) Find the slope of the line. As we go from ( -8,-6) to (12,9), x increases by 20 and y increases by 15. Thus, the slope, m, is m = rise / run = 15/20 = 3/4
2) Recognize that the y-intercept is zero (0) because this is direct variation; the line goes thru the origin.
3) write the equation of the line: y = mx + b becomes y = (3/4)x
[tex]\bf (\stackrel{x_1}{-8}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-6)}{12-(-8)}\implies \cfrac{9+6}{12+8}\implies \cfrac{15}{20}\implies \cfrac{3}{4}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-6)=\cfrac{3}{4}[x-(-8)]\implies y+6=\cfrac{3}{4}(x+8) \\\\\\ y+6=\cfrac{3}{4}x+6\implies y=\cfrac{3}{4}x[/tex]
Find the tenth term in the following geometric sequence. 8, 4, 2, 1, . . .
a) 13
b) 0.0078
c) 0.0156
d) 12.5
Answer:
c) 0.0156
Step-by-step explanation:
The general term a[n] of a geometric sequence is given in terms of the first term a[1] and common ratio r as ...
a[n] = a[1]r^(n-1)
The given sequence has an initial term of a[1]=8 and a common ratio of 4/8=1/2. Then the general term is ...
a[n] = 8(1/2)^(n-1)
The 10th term is then ...
a[10] = 8(1/2)^(10-1) = 8(1/2)^9 = 8/512
a[10] = 0.015625 ≈ 0.0156
Find the perimeter and the area of the composite figure
a. What is the approximate perimeter of the concrete region? Use 3.14 for π
b. What is the exact area of the concrete region? Leave answers in terms of π.
Answer:
Part A) The approximate perimeter of the concrete region is [tex]P=64.66\ yd[/tex]
Par B) The exact area of the concrete region is [tex]A=(8\pi+162.4)\ yd^{2}[/tex]
Step-by-step explanation:
Part A) What is the approximate perimeter of the concrete region?
we know that
The perimeter of the composite figure is equal to
[tex]P=\pi r+2(15.2)+ 11.5+10.2[/tex]
The radius of semicircle is
[tex]r=8/2=4\ yd[/tex]
substitute
[tex]P=(3.14)(4)+2(15.2)+ 11.5+10.2=64.66\ yd[/tex]
Part B) What is the exact area of the concrete region?
we know that
The area of the composite figure is equal to the area of semicircle plus the area of rectangle plus the area of triangle
so
[tex]A=\frac{1}{2} \pi r^{2} +(15.2)(8)+\frac{1}{2}(10.2)(8)[/tex]
The radius of semicircle is
[tex]r=8/2=4\ yd[/tex]
[tex]A=\frac{1}{2} \pi (4)^{2} +(15.2)(8)+\frac{1}{2}(10.2)(8)[/tex]
[tex]A=8\pi+121.6+40.8[/tex]
[tex]A=(8\pi+162.4)\ yd^{2}[/tex]
The function k(x) = (g · h)(x) is graphed below, where g is an exponential function and h is a linear function.
If g(x) = -3 x , which option below give the formula for h?
A.) h(x) = -3x
B.) h(x) = -2x
C.) h(x) = 2x
D.) h(x) = 3x
Without the equation for k(x), we can't definitively determine the formula for h(x). However, if we knew k(x), we'd divide it by g(x) (-3x in this case) to find h(x). For instance, if k(x) is 6x, h(x) will be -2.
Explanation:To find the formula for h, we need to divide k(x) by g(x). The formula for the function k should be given in addition to the graph in order for us to solve this. Assuming that g(x) is indeed -3x, we would divide the formula for k(x) by -3x to find h(x). However, without the expression for k(x), we can't definitively select an option for h(x) from your list.
Example:
If k(x) was 6x, and g(x) was -3x, h(x) would be -2. You would find this by dividing k(x), which is 6x, by g(x), which is -3x; resulting in -2. So, for this example, option B would be correct.
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At Dante party 16 children share 192 crayons. At Maria party 13 children share 234 crayons. Each party splits the crayons equally among the children attending. How many more crayons does each child at Maria's party get than each child at Dante's party?
Answer:
Each child in Maria's party got 6 crayons more that each child in Dante's party
Explanation:
1- In Dante's party:
192 crayons are equally split among 16 children
This means that:
Each child got [tex]\frac{192}{16} = 12[/tex] crayons
2- In Maria's party:
234 crayons are equally split among 13 children
This means that:
Each child got [tex]\frac{234}{13}=18[/tex] crayons
3- getting the difference:
Difference = 18 - 12 = 6 crayons
This means that:
Each child in Maria's party got 6 crayons more that each child in Dante's party
Hope this helps :)
If you horizontally stretch the quadratic parent function f(x)=x^2 by a factor of 3. What is the equation
Answer:
G(x)=(1/3x)^2
Step-by-step explanation:
Ap ex
what is the value of c such that x^2-20x+c is a perfect-square trinomial?
Answer:
c=100
Step-by-step explanation:
To complete the square, it would really help if the coefficient of x^2 is 1 which is so formula for c in this case is just (b/2)^2
So (-20/2)^2
simplifying gives
(-10)^2
100
c=100
Answer:
100
Step-by-step explanation:
The question is on making the equation a perfect square
Given ;
[tex]x^2 - 20x + c[/tex]
To get c;
[tex]c=(\frac{b}{2} )^2[/tex]
where ;
[tex]b= -20[/tex]
[tex]c= (\frac{-20}{2} )^2 = 10^2 = 100[/tex]
Which of the following constants can be added to x 2 - x to form a perfect square trinomial?
A) 1/4
B) 1/2
C) 1
Can someone help me with this question
5 gallons 3 quarts + 4 gallons 2 quarts=?
Step-by-step explanation:
5 gallons 3 quarts +4 gallons 2 quarts
5.3
+
4.2
=9.5 gallons
Answer: 10 gallons and 1 quart.
Explanation: 5 gallons + 4 gallons = 9 gallons. 3 quarts + 2 quarts = 5 quarts, and 4 quarts make a gallon. So, 10 gallons and 1 quart.
Janet and Nadia each play basketball. Nadia has won twice the number of games Janet has. Is it possible for Janet to have won 10 games if the sum of the games Nadia and Janet have won together is 24?
Answer: It is not possible for Janet to have won 10 games.
Step-by-step explanation:
Let be "x" the number of games Janet won.
We know that Nadia has won twice the number of games Janet has and the sum of the games Nadia and Janet have won together is 24.
Then, we express this situation with this equation:
[tex]x+2x=24[/tex]
So, let's check if it is possible for Janet to have won 10 games. Substitute [tex]x=10[/tex] into the expression:
[tex]10+2(10)=24\\\\10+20=24\\\\30=24\ (This\ is\ not\ true)[/tex]
Therefore, it is not possible for Janet to have won 10 games.
Answer:
not possible
Step-by-step explanation:
Let be "x" the number of games Janet won.
We know that Nadia has won twice the number of games Janet has and the sum of the games Nadia and Janet have won together is 24.
Then, we express this situation with this equation:
So, let's check if it is possible for Janet to have won 10 games. Substitute into the expression:
Therefore, it is not possible for Janet to have won 10 games.
Will give brainliest
Series to Sigma Notation
Write the following series in sigma notation.
6+10+14+18+22+26+30
Example image shown below.
[tex]\displaystyle\\\sum_{n=1}^7(4n+2)[/tex]
Need help with finding the value of x
Answer:
The value of x = 4.1 cm
Step-by-step explanation:
From the figure we can see a circle, with chord 15.6 cm
A right angled triangle with hypotenuse 8.8 cm
To find the value of x
By using Pythagorean theorem,
Base² + Height² = Hypotenuse²
Here Base = x, Height = 15.6/2 = 7.8 cm and Hypotenuse = 8.8 cm
x² + 7.8² = 8.8²
x² = 8.8² - 7.8²
= 77.4 - 60.84
= 16.56
x = √16.56 = 4.07 ≈ 4.1 cm
Therefore the value of x = 4.1 cm
(.......) is an example of :?
For this case we have that by definition the distributive property establishes:
[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]
We have the following expression:
[tex](y ^ 2 + y) (x ^ 4 + 3x ^ 3-2x ^ 3) =[/tex]
Applying the distributive property we have:
[tex]y ^ 2 (x ^ 4 + 3x ^ 3-2x ^ 3) + y (x ^ 4 + 3x ^ 3-2x ^ 3)[/tex]
So, the given example is an example of distributive property.
ANswer:
Option B
URGENT NEED HELP WITH A MATH QUESTION
Answer:
The image of point P is (1 , -1)
Step-by-step explanation:
- If point (x , y) rotated about the origin by angle 90° anti-clock wise
∴ Its image is (-y , x)
- If point (x , y) rotated about the origin by angle 90° clock wise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 180°
∴ Its image is (-x , -y)
* There is no difference between rotating 180° clockwise or
anti-clockwise around the origin
* Lets solve the problem
∵ P = (-1 , -1)
∵ P is rotated about the origin 90° counterclockwise
- Lets use this rule:
If point (x , y) rotated about the origin by angle 90° counterclockwise
then Its image is (-y , x)
∵ x-coordinate of point P = -1
∴ y-coordinate of the image of point P is -1
∵ y-coordinate of point P is -1
∴ x-coordinate of the image of point P is 1
- Lets write the image of point P
∴ The image of point P is (1 , -1)