The supplied lines' point of intersection has the x coordinate is 6.
What is coordinate geometry?A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.
The x coordinate of the location where the ensuing lines intersect must be chosen.
3x + 5y = 78 ...........................(1)
2x - y = 0 ...............................(2)
The given system of equations must be solved in order to determine the x coordinate of the site of intersection.
Equation (ii) provides us with
2x = y
y = 2x ........................(3)
Equation I yields the result when the value of y from equation (iii) is substituted.
3x + 5(2x) = 78
3x + 10x = 78
13x = 78
x = 78/13
x = 6.
As a result, the supplied lines' point of intersection has the x coordinate 6.
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I understand that the question you are looking is :
3x 5y = 78 2x - y = 0 the point of intersection of the lines has an x-coordinate of _____.
A. 7
B.8
C. 6
D. -6
PLS HELP. I tried and cant figure it out.
Answer:
I x² +12x I = -32
Step-by-step explanation:
Absolute value equation:
x = -4 ; x = -8
x + 4 = 0 and x + 8 = 0
(x +4)(x + 8) = 0
x*x + x*8 + 4*x + 4*8 = 0
x² + 4x + 8x + 32 = 0
x² + 12x + 32 = 0
Absolute value equation:
I x² + 12x I = -32
Select the correct answer. create a matrix for this linear system: what is the solution of the system?
The complete question is:
Create a matrix for this linear system:
what is the solution of the system?
[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]
The solution straight from the matrix as
[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]
[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex]
and z = r
What is the solution of the system?A solution to a system of equations exists a set of values for the variable that satisfy all the equations simultaneously.
Given:
[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]
By applying two more row operations, we get
[tex]$&{\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\2 & 3 & -1 & -2\end{array}\right] R_{2}+(-2) R_{1} \rightarrow R_{2}} \\[/tex]
[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 5 & 3 & -4\end{array}\right] \frac{1}{5} R_{2} \rightarrow R_{2} \\[/tex]
simplifying the above matrix, we get
[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right] R_{1}+R_{2} \rightarrow R_{1} \\[/tex]
[tex]$&\equiv\left[\begin{array}{rrr|r}1 & 0 & -\frac{7}{5} & \frac{1}{5} \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right]$$[/tex]
The solution straight from the matrix as
[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]
[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex] and
z = r
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(2x² – 3x)(3x² + 2x - 1)
Answer:
6x^4-5x^3-8x^2+3x
Step-by-step explanation:
-factor it using FOIL (first outside inside last)
Given the following information, calculate the perimeter of triangle RST. Assume triangle RZX is similar to triangle RST.
RZ = 21, RY = 24, RX = 42, ZY = 9, and SW = 15.
Check the picture below.
Express graph in slope intercept form
Answer:
2/6
Step-by-step explanation:
Count up and over going from one point to the next and you get slope intercept. This one is up 2 over 6
Answer:
y = 1/3x - 3
Step-by-step explanation:
Slope-intercept form follows the format y = mx + b, where m is the slope of the line, and b is the y-intercept.
First let's find the slope. The slope is the amount the graph rises/runs. From point (0,-3), it rises by 1, and runs to the right by 3 where it meets the next point on the graph, meaning that the slope is 1/3.
Now, let's find the y-intercept. The y-intercept is the point on the graph where the line touches the y-axis. In this line, we can clearly see that the line touches (0,-3), therefore, the y-intercept is -3.
Using this information, we can construct the equation y = 1/3x - 3
Micheal was asked to give examples of the identity property of addition and the identity property of multiplication. Below are his answers. Identity property of addition: 8 + 1 = 8 identity property of multiplication: 8(0) = 0 What was his mistake
Answer:
Identity property of addition 8 + 0 = 8
Identity property of multiplication 8 x 1 = 8
Step-by-step explanation:
He mixed up his properties. 8 + 1 does not equal 8. I want to know what I can add to 8 and that I would still get 8, the answer is zero.
The identity property of multiplication is showing that any number multiplied by 1 is itself.
Simplify the expression:
-2(-1 + 2w) =
Submit please
[tex]-2(-1+2w)[/tex]
distribute
[tex]2-4w[/tex]
put in standard form
[tex]-4w+2[/tex]
Refer to the figure to the right.
A. If RV RT, name two congruent angles.
B. If RSSV, name two congruent angles.
C. If LSRT LSTR, name two congruent segments.
D. If LSTV= LSVT, name two congruent segments.
R
T
Answer:
c if lsrt lstr name two congruent segments
A rental truck company charges a flat fee of $30 to rent a truck in addition to $0.25 per miles how much would it cost to rent a van for 80 miles
Answer:
$50
Step-by-step explanation:
x is distance and y is cost because the cost is dependent on the distance which makes the distance the independent variable. you can always use y=mx+b for these problems!!
A shipment of inexpensive digital watches, including that are defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be rejected?.
0.8926 percent of the time, the shipment will be rejected.
What is Probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
According to the given information:A delivery of 50 cheap digital watches, 10 of which are flawed.
A digital watch's likelihood of malfunctioning
P = 10/50
= 0.2
Size of sample: n = 10
Additionally, if they find one or more samples to be defective, they reject the entire cargo.
Making use of the binomial probability formula:
[tex]P(x)={ }^{n} C_{x} p^{x}(1-p)^{n-x}[/tex]
The random variable x should stand in for the quantity of defective watches.
The chance that the delivery will be refused is:
[tex]\begin{aligned}&P(x \geq 1)=1-P(0) \\&=1-{ }^{10} C_{0}(0.2)^{0}(0.8)^{10}\end{aligned}[/tex]
= 1 - (0.8)
= 0.8926
As a result, 0.8926 percent of the time, the shipment will be rejected.
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I understand that the question you are looking for is:
A shipment of 50 inexpensive digital watches, including 10 that are defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be rejected
How to do this question. First to answer this question will be marked as brainlist.
Answer:
10
Step-by-step explanation:
Every number with exponent zero is equal to 1
(7³×8)⁰ = 1
5⁰ = 1
then:
(3² + 5⁰) / (7³×8)⁰
= (3² + 1) / 1
= (9+1) / 1
= 10
3^2 = 9
3^2 = 95^0 =1
(7^3 x 8)^0 is 1
(anything to power of zero is one)
9 + 1 / 1 gives us the fraction 10/1
10/1 + 1/3 => make denominator the same, so I'll multiply 10/1 by 3
We get : 30/3 + 1/3 => 31/3
Thus answer is 31/3
Hope this helps!
What is the solution to the
system of equations graphed below?
y = x- 2
y = 3x - 2
Answer:
(0, -2)
Step-by-step explanation:
The solution to a system of equations is the point on the graph where the lines intersect.
SolutionHere, both lines have a y-intercept of -2, so intersect there. The solution is ...
(x, y) = (0, -2)
Find the length of AN given the figure below:
Answer:
21
Step-by-step explanation:
In the diagram, the three tangents (segment touching a circle at one point) have equal length.
6y - 3 = 29 - 2y
8y = 32
y = 4
Since the lengths of segments AM and AN are equivalent, we can substitute the value of y into the expression, 6y - 3, to find AN.
6y - 3 = 6*4 - 3 = 24 - 3 = 21
A gardener uses 1/3 of a liter of water to water 2/7 of a garden.
Answer:
[tex]\boxed{\sf 1\dfrac{1}{6}\ liters \ of \ water}[/tex]
Explanation:
Let the total water required water the entire ground be g
Equation:
[tex]\sf \dfrac{2}{7}\:g = \dfrac{1}{3} \ liters \ of \ water[/tex]
rearranging
[tex]\sf g = \dfrac{7(1)}{3(2)}[/tex]
simplify
[tex]\sf g = \dfrac{7}{6} \ liters \ of \ water[/tex]
rewrite in mixed fraction
[tex]\bf g = 1\dfrac{1}{6}\ liters \ of \ water[/tex]
The water required to water the entire ground is 1 1/6 liters.
Which test point holds true for the inequality 3/2y-2x>=1? Where does the shaded area lie for this inequality? The test point holds true for this inequality. The shaded area for the inequality lies the boundary line.
The test That holds true for this inequality is given as 1/4 and 1
How to solve for the inequality3/2 y - 2x > 1
The goal is to make y the subject
then
3/2 y > 2x + 1
We have to divide through the equation by 3/2
Such that y > 4/3 x + 2/3
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The exterior surface of a farm silo needs to be painted. if one gallon of paint covers 224 square feet, what is the minimum number of gallons needed to paint the silo? keep in mind that the bottom of the silo is not painted. use π = 3.14
The gallons needed to paint the silo is 10.
How many gallons is needed to paint the silo?A cylinder is a three-dimensional object. It is a prism with a circular base. The total surface area of cylinder can be determined by adding the area of all its faces.
Total surface area of the cylinder excluding its base = 2πrh +πr²
Where:
r = radius h = heightTSA = (2 x 3.14 x 10 x 30) + (3.14 x 10²)
314 + 1884 = 2198 ft²
Number of gallons needed = 2198 / 224 = 9.81 = 10 gallons
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john is constructing a satellite dish . The receiver is going to be located 15 inches above the vertex of the dish. The dish is going to be 84 inches wide. How deep will the dish be
The depth of the 84 inches wide satellite dish that has the receiver located 15 inches above the vertex is 29.4 inches.
How can the equations of a parabola be used to find the depth of the dish?The location of the receiver = 15 inches above the vertex
Width of the dish = 84 inches
The receiver of a satellite dish is normally located at the focus (focal point).
Taking the shape of the satellite dish as a parabola, and writing the equation of the parabola as x² = 4•a•y, we have;
Coordinates of the focus = (0, a)
Where;
a = The distance of the focus above the vertex
Therefore;
a = 15 inches
The dish is horizontally spaced equally about the vertex.
The farthest point horizontally from the vertex, X, of the dish corresponds to the furthest vertically from the vertex, which is the maximum depth or height, Y.
At the maximum height, from the vertex, Y, (farthest point, vertically from the vertex), we have;
X = 84 ÷ 2 = 42
Which gives;
42² = 4 × 15 × Y
Y = 42² ÷ (4 × 15) = 29.4
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An interior angle of a regular polygon has a measure of 108°. What type of polygon is it?
The polygon is
Answer:
a polygon with an interior angle of 108 is a pentagon
Mr. jimenez deposited money into an account in which interest is compounded quarterly at a rate of 2.6%. how much did he deposit if the total amount in his account after 4 years was $7160.06, and he made no other deposits or withdrawals? $6455 $6455 $6798 $6798 $6887 $6887 $6977 $6977 skip to navigation
Answer:
$6455.
Step-by-step explanation:
The formula for this investment is:
A = P(1 + r/4)^4t where P = amount deposited , A amount after t years,
r = rate (as a decimal fraction).
So we have:
7160.06 = P(1 + 0.026/4)^16
7160.06 = P * 1.109227
P = 7160.06 / 1.109227
= $6455.
Which point lies on the line described by the equation below? y+4=4(x-3
[tex]\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 \begin{array}{llll} y+4=4(x-3)\implies y-(\stackrel{y_1}{-4})=\stackrel{m}{4}(x-\stackrel{x_1}{3})\\\\ ~\hfill (\stackrel{x_1}{3}~~,~~\stackrel{y_1}{-4}) \end{array}[/tex]
Zoey read a novel in 30 days she made it a habit to read 13 pages everyday for the first 20 days. if in the last 10 days she reads 6 pages everyday how many pages are in the book?
Answer:
320 pages.
Step-by-step explanation:
We can simply multiply and add to find how many pages are in the book.
So we have (13 pg * 20 d) + (6 pg * 10 d) = 260 + 60 = 320.
Another way of solving is to set up a proportion for both the 20 and 10 days, find how many pages are read on these days, and add:
[tex]\frac{13pg}{1d}=\frac{xpg}{20d}\\ x=260pages\\\\\frac{6pg}{1d} =\frac{xpg}{10d}\\ x=60pg\\260+60=320[/tex]
The perimeter of a rectangle is 320 feet. Find the length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.
The length is 25 feet and the width is 135 feet
What are consecutive odd integers?
Consecutive odd integers differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers.
How to find the perimeter of the rectangle?
⇒Perimeter of rectangle = 2(l+w)
The perimeter of a rectangle is 320 feet
let the length of a rectangle is x
The next consecutive odd integer is x+2
width = 5(x+2)
=5x+10
2(length + width) = 320
l+w=160
x+5x+10=160
6x=150
x=25
length = 25 feet
width = 5(25+2)=135 feet
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A clock has a diameter of 16 inches. How far does the hour hand travel during 5 hours? Use 3.14 for pi.
Therefore the hour hand travels 40.192in in 5 hours
A sector is said to be a part of a circle made of the arc of the circle along with its two radii.
The formula for calculating the area of a sector is expressed as;
A = r²β/2
where
r is the radius of the circle
β is the angle subtended
Since the the hour hand travel during 5 hours, the subtended angle by the sector will be;
β = 360/5
β = 72 degrees
Given the following parameters
r = 16/2
r = 8in
Substitute into the formula
A = 8²(72π)/360
A = 40.192in
Therefore the hour hand travels 40.192in in 5 hours
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what is the solution to this equation 7x-3(x-6)=30
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
⨠ use the distributive property
[tex]\sf{7x-3(x-6)=30}[/tex]
[tex]\sf{7x-3x+18=30}[/tex]
⨠ combine like terms
[tex]\sf{4x+18=30}[/tex]
⨠ subtract both sides by 18
[tex]\sf{4x=30-18}[/tex]
[tex]\sf{4x=12}[/tex]
⨠ divide both sides by 4
[tex]\boxed{\sf x=3}[/tex]
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices.
Josiah’s Music
Sample 1
Sample 2
R & B
5
R & B
4
Pop
4
Pop
3
Classical
3
Classical
5
Jazz
2
Jazz
4
Rock
6
Rock
4
Josiah’s work:
StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x.
He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
He did not multiply the numerator and denominator by the correct number to equal 1,500.
His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion.
He can only solve the proportion by multiplying the numerator and denominator by a common multiple.
He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Based on the number of songs in each genre that Josiah listened to, the statements about his solution that are true are:
He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.He did not multiply the numerator and denominator by the correct number to equal 1,500.He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.What did Josiah do wrong?To find the average of the number of rock songs, he should have taken the average of rock songs he listened to which were 4 and 6:
= (4 + 6) / 2
= 5
Because he has a total of 1,500 songs on his player, he should have multiplied both the numerator and denominator by a number that would lead to 1,500 which is 75 and not 30.
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What is the probability that two people have a birthday in May?
Step-by-step explanation:
There is 31 days in May so the probability is
[tex]p(bday \: in \: may) = \frac{2}{31} [/tex]
1. Solve for x.
12
10
X
5
In the regular octagon below, if AP = 12 cm. and BC = 19 cm, find its area.
First symmetrically cut the octagon to get 8 pieces. (So that you will get the idea that this polygon is divided into 8 triangles)
Then find the area of one of the triangles:
Area of Triangle = [tex]\frac{1}{2} * b* h[/tex]
A = [tex]\frac{1}{2}[/tex] × 12 × 19
A = 114 cm²
To find the area of the whole octagon shape:
A = 114 × 8 = 912 cm²
Hope it helps!
Answer:
Step-by-step explanation:
You cannot do this unless you are certain that P is the center of the octagon. I don't know if that's solvable from the information given. So I will make the assumption that P is the center.
Determine the midpoint of BC. Call it E. Draw a line from P to E. By symmetry EP = AP. BE = 1/2 * BC = 19/2 = 9.5 by construction
You have a trapezoid witch is 1/4 the area of the octagon. Three more trapezoids can fit into the octagon.
Formula
Area = (AP + BE)*PE / 2
Givens
AP = 12
BE = 9.5
PE = 12
Solution
Put the givens and constructions into the formula
Area = (12 + 9.5)*12/2
Area = 21.5 * 12/2
Area = 21.5 * 6
Area = 129
That's the area of one of the trapezoids. Multiply the area here by 4.
You get 516.
a group of preschoolers has 2 boys and 30 girls. what os the ratio of boys to all childern
Answer:
1 boy to 15 girls.
Step-by-step explanation:
Since there is only two boys, I divided each number by two and got 1 to 15. Have an amazing day!
The ratio of boys to all children in the group is 1:16.
Given that in a group there are 2 boys and 30 girls.
We need to find the ratio of boys to all children.
To find the ratio of boys to all children in the group, we need to add the number of boys and girls together to get the total number of children.
Then, we can express the number of boys as a fraction of the total number of children.
Number of boys = 2
Number of girls = 30
Total number of children = Number of boys + Number of girls
Total number of children = 2 + 30 = 32
Now, we can express the number of boys as a fraction of the total number of children:
Ratio of boys to all children = Number of boys / Total number of children
Ratio of boys to all children = 2 / 32
To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
Ratio of boys to all children = 1 / 16
So, the ratio of boys to all children in the group is 1:16.
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What are the values of the three trigonometric ratios for angle l, in simplest form? sin(l) = 4/5 cos(l) = 3/5 tan(l) = 4/3
The values of the three trigonometric ratios for angle L, in simplest form, are:
[tex]sin(L)=\frac{4}{5}[/tex][tex]cos(L)=\frac{3}{5}[/tex][tex]tan(L)=\frac{4}{3}[/tex]To find the values of the three trigonometric ratios for angle L, in the simplest form:Given -
The triangle LMN is given in the question.
The measurement of side LM is 15 unitsThe measurement of side LN is 25 unitsThe measurement of side MN is 20 unitsAs the trigonometric properties of a triangle state that the value of sin, cos, and tan for the respective angle can be written as:
sin(L) = perpendicular / hypotenusecos(L) = base / hypotenusetan(L) = perpendicular / baseUsing the above trigonometric properties, the value of sin(L):
[tex]sin(L) =\frac{20}{25} =\frac{4}{5}[/tex]Similarly, the value of cos(L):
[tex]cos(L)=\frac{15}{25} =\frac{3}{5}[/tex]And, the value of tan(L) is:
[tex]tan(L)=\frac{20}{15} =\frac{4}{3}[/tex]Therefore, the values of the three trigonometric ratios for angle L, in simplest form, are:
[tex]sin(L)=\frac{4}{5}[/tex][tex]cos(L)=\frac{3}{5}[/tex][tex]tan(L)=\frac{4}{3}[/tex]Know more about trigonometric ratios here:
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The question you are looking for is given below:
What are the values of the three trigonometric ratios for angle L, in simplest form?
