The value of x = -1
The value of y = -5
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be A
The value of A is
y = 3x - 2 be equation (1)
Let the second equation be B
The value of B is
x - y = 4 be equation (2)
On simplifying equation (2) , we get
Adding y on both sides of the equation , we get
x = y + 4 be equation (3)
Substituting the value of x in equation (1) , we get
y = 3x - 2
y = 3 ( y + 4 ) - 2
y = 3y + 12 - 2
y = 3y + 10
Subtracting y on both sides of the equation , we get
2y + 10 = 0
Subtracting 10 on both sides of the equation , we get
2y = -10
Divide by 2 on both sides of the equation , we get
y = -5
Substitute the value of y in equation (3) , we get
x = y + 4
x = -5 + 4
x = -1
Therefore , the value of x is -1 and the value of y is -5
Hence , The value of x = -1
The value of y = -5
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Final answer:
To solve the equations using substitution, isolate y from the first equation, substitute it into the second, solve for x, and then use the value of x to find y. The solution to the system is x = -1 and y = -5.
Explanation:
To solve the system of equations by substitution, we will first isolate y in one of the equations and then substitute it into the other equation.
Step 1: Isolate y in the first equation.
We have y = 3x - 2. This equation is already solved for y, so we can use it as our substitution.
Step 2: Substitute y into the second equation.
Our second equation is x - y = 4. We substitute y with 3x - 2 to get x - (3x - 2) = 4.
Step 3: Solve for x.
Now, we simplify and solve for x:
x - 3x + 2 = 4
-2x + 2 = 4
-2x = 4 - 2
-2x = 2
x = -1
Step 4: Substitute x back into the first equation to solve for y.
Using x = -1 in the first equation y = 3x - 2, we get:
y = 3(-1) - 2
y = -3 - 2
y = -5
Therefore, the solution to the system of equations is x = -1 and y = -5.
Write the equation of the line that passes
through the points (0,-5) and (1,-9).
I’m stuck....:(
Answer:
The slope is -4.
Step-by-step explanation:
Slope formula:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex]
[tex]\displaystyle \frac{(-9)-(-5)}{1-0}=\frac{-4}{1}=-4[/tex]
Therefore, the slope is -4, and the correct answer is -4.
Hope this helps!
What is the slope-intercept equation for the line below?
(4.1)
(0, -4)
Answer:
y=5/4x-4
Step-by-step explanation:
C. y = 5/4x - 4.
What is slope-intercept?One of the three ways we may express a straight line is in slope-intercept form. The other forms are known as point slope form and standard form, however in this section we will mostly use slope-intercept form. The slope-intercept form is used to write a line's equation as y = mx + c.
You may be aware that a point's coordinates on a graph are x and y.
Given two coordinates of a line from that, we can calculate the slope.
slope m = (y₂ - y₁) / (x₂- x₁)
m = 5/4
Put the value of m and one coordinate value in the slope-intercept equation
-4 = 5/4 * 0 + c
c = -4
therefore slope-intercept equation of given coordinates is y = 5/4x - 4.
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Jackrabbit are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second
Answer:
58.6667
Step-by-step explanation:
if you see there are 5280 ft in 1 mile so use ur brain
Answer:
58.67 feet per second.
Step-by-step explanation:
We have been given that Jackrabbit are capable of reaching speeds up to 40 miles per hour. We are asked to represent this speed in feet per second.
We know that 1 mile equals 5280 feet.
We also know that 1 hour equals 3600 seconds.
[tex]\text{Speed of jackrabbit}=\frac{\text{40 miles}}{\text{Hour}}\times \frac{\text{5280 feet}}{\text{Mile}}\times \frac{\text{1 hour}}{\text{3600 sec}}[/tex]
[tex]\text{Speed of jackrabbit}=\frac{40 \times\text{5280 feet}}{\text{3600 sec}}[/tex]
[tex]\text{Speed of jackrabbit}=\frac{211200\text{ feet}}{\text{3600 sec}}[/tex]
[tex]\text{Speed of jackrabbit}=\frac{58.67\text{ feet}}{\text{3600 sec}}[/tex]
Therefore, the speed of jackrabbit is 58.67 feet per second.
the slope is -4 which of the following is the point -slope form of the line (2,-8)
[tex]\huge{\boxed{y+8=-4(x-2)}}[/tex]
Point slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is any point on the line.
We can simply plug in the values. [tex]y-(-8)=-4(x-2)[/tex]
Then, just simplify the negative subtraction. [tex]y+8=-4(x-2)[/tex]
Distance between points (-1,2) and (3,-5)
[tex]\huge{\boxed{\sqrt{65}}}\ \ \boxed{\text{approx. 8.06225775}}[/tex]
The distance formula is [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the points.
Substitute in the values. [tex]\sqrt{(3-(-1))^2 + (-5-2)^2}[/tex]
Simplify the negative subtraction. [tex]\sqrt{(3+1)^2 + (-5-2)^2}[/tex]
Add and subtract. [tex]\sqrt{4^2 + (-7)^2}[/tex]
Solve the exponents. [tex]\sqrt{16 + 49}[/tex]
Add. [tex]\sqrt{65}[/tex]
[tex]65[/tex] has no square factors, so this is as simple as the answer can get. You can use a calculator to find that [tex]\sqrt{65}[/tex] is approximately [tex]8.06225775[/tex].
The formula for distance between two points is:
[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}[/tex]
In this case:
[tex]x_{2} =3\\x_{1} =-1\\y_{2} =-5\\y_{1} =2[/tex]
^^^Plug these numbers into the formula for distance like so...
[tex]\sqrt{(3 -(-1))^{2} + (-5-2)^{2}}[/tex]
To solve this you must use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)
First we have parentheses. Remember that when solving you must go from left to right
[tex]\sqrt{(3 -(-1))^{2} + (-5-2)^{2}}[/tex]
3 - (-1) = 4
[tex]\sqrt{(4)^{2} + (-5-2)^{2}}[/tex]
-5 - 2 = -7
[tex]\sqrt{(4)^{2} + (-7)^{2}}[/tex]
Next solve the exponent. Again, you must do this from left to right
[tex]\sqrt{(4)^{2} + (-7)^{2}}[/tex]
4² = 16
[tex]\sqrt{16 + (-7)^{2}}[/tex]
(-7)² = 49
[tex]\sqrt{(16 + 49)}[/tex]
Now for the addition
[tex]\sqrt{(16 + 49)}[/tex]
16 + 49 = 65
√65 <<<This can not be further simplified so this is your exact answer
Your approximate answer would be about 8.06
***Remember that the above answers are in terms of units
Hope this helped!
~Just a girl in love with Shawn Mendes
The graph below shows the solution for the following system.
{f(x)=2x−3
g(x)=2^x−4
Linear function passing through (0, negative 3), (1.5, 0) & about (2.7, 2.3).
Exponential function passing through (negative 3, negative 4), (0, negative 3), (2,0) & about (2.7, 2.3).
Which statements are true?
Select all that apply.
x=0 is a solution to the system.
(1.5,0) and (2,0) are solutions to the system because the graphs of f(x) and g(x) cross the x-axis at those points.
When x≈2.7, the graphs of f(x) and g(x) intersect because they are equal to each other at that value.
f(x)=g(x) when x=0.
Answer:
TRUE:
When x≈2.7, the graphs of f(x) and g(x) intersect
f(x)=g(x) when x=0
Step-by-step explanation:
The graphs of two function y=f(x) and y=g(x) are shown in attached diagram.
These two graphs intersect at two points (0,-3) and about (2.7,2.3). This means that
f(0)=g(0)=-3
and
f(2.7)=g(2.7)=2.3
So, x=0, y=-3 is the solution to the system (the solution to the system is ordered pair (x,y), not only x)
Points (1.5,0) and (2,0) are not solutions, because they are not points of graphs intersection.
When x≈2.7, the graphs of f(x) and g(x) intersect (TRUE)
f(x)=g(x) when x=0 (TRUE)
Answer:
f(x)=g(x) when x=0.
x=0 is a solution to the system.
When x≈2.7, the graphs of f(x) and g(x)intersect because they are equal to each other at that value.
What is the x-interception of the Logarithmic function??
The answer is:
Why?To find the x-interception of the given function, we just need to isolate the variable "x", by making the function (y) equal to 0.
So, we are given the function:
[tex]F(x)=y=Log_{0.71}(x)[/tex]
Now, making y equal to 0, to isolate "x", we have:
[tex]y=Log_{0.71}(x)\\\\0=Log_{0.71}(x)[/tex]
[tex]0=Log_{0.71}(x)\\\\0.71^{0}=0.71^{Log_{0.71}(x)}} \\\\1=x[/tex]
We have that the x-intercept of the logarithmic function is located at (1,0)
Hence, the correct answer is:
B. (1,0).
Have a nice day!
Note: I have attached a picture for better understanding.
i need help asap thank you
Answer:
363
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
d = - 85 - (- 92) = - 85 + 92 = 7 and a₁ = - 92, hence
[tex]a_{66}[/tex] = - 92 + (65 × 7 ) = - 92 + 455 = 363
nine times five less than twice x
Answer:
3
Step-by-step explanation:
For this case we must express algebraically the following sentence:
"Nine times five less than twice x"
We have to:
Nine times five represents: [tex]9 * 5 = 45[/tex]
Twice x represents:[tex]2x[/tex]
So we have that "Nine times five less than twice x" is represented as:
[tex]2x-45[/tex]
Answer:
[tex]2x-45[/tex]
What is the following product 3 square root 2(5 square root 6-7 square root 3
Answer:
30√3 - 21 √6
Step-by-step explanation:
The given expression is:
3√2 (5√6 -7√3)
We cannot subtract the values inside the bracket because the values inside the radicals are not same.
So multiply 3√2 with the bracket.
=3*5√2*6 - 3*7√2*3
=15√12 - 21√6
Now break √12
=15√4*3 - 21√6
write √4*3 separately:
=15√4 *√3 - 21√6
We know that √4 = 2
=15*2*√3 - 21√6
=30√3 - 21 √6
Therefore the answer is 30√3 - 21 √6 ....
Find the area of the shaded region.
Round to the nearest tenth.
9.28 cm
68.90
Area = [?] cm?
I really need help pretty quick on this one. So plz hurry if u can.
Answer:
The area of the shaded region is [tex]11.6\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the sector of circle of angle 68.9 degrees minus the area of the isosceles triangle
step 1
Find the area of sector of the circle
The area of circle is equal to
[tex]A=\pi r^{2}[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]r=9.28\ cm[/tex]
substitute
[tex]A=(3.14)(9.28)^{2}[/tex]
[tex]A=270.41\ cm^{2}[/tex]
Remember that the area of a circle subtends a central angle of 360 degrees
so
using proportion Find out the area of a sector with a central angle of 68.90 degrees
Let
x -----> the area of a sector
[tex]270.41/360=x/68.90\\\\x=68.90*270.41/360\\\\x=51.75\ cm^{2}[/tex]
step 2
Find the area of the isosceles triangle
Applying the law of sines
The area is equal to
[tex]A=(1/2)r^{2}sin(68.90)[/tex]
we have
[tex]r=9.28\ cm[/tex]
substitute
[tex]A=(1/2)(9.28)^{2}sin(68.90)=40.17\ cm^{2}[/tex]
step 3
Find the area of the shaded region
[tex]51.75-40.17=11.58\ cm^{2}[/tex]
Round to the nearest tenth
[tex]11.58=11.6\ cm^{2}[/tex]
The calculated area of the shaded region is 11.6 square cm
How to determine the area of the shaded region.from the question, we have the following parameters that can be used in our computation:
The circle
The area of the shaded region is calculated as
Area of shaded region = Area of sector - Area of triangle
Using the respective formulas, we have
Area of shaded region = 68.9/360 * 3.14 * 9.28 * 9.28 - 1/2 * 9.28 * 9.28 * sin(68.9)
Evaluate
Area of shaded region = 11.6
Hence, the area of the shaded region is 11.6 square cm
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Find the percentage of data points that lie between -3.01 and 2.61?
z= (x-u) /o
Answer:
To find the percetage of data points that lie between the points -3.01 and 2.61, on a normal distribution we're going to need the help of a calculator. The result is: 99.42%
Attached you will find the graph that represents the result.
6/22 to the nearest whole percent?
is?
1) Divide the numbers
6/22= 0.27 (27 is repeating)
2) Multiply the decimal by 100
0.2727(100)= 27.27
3) Round
27.27 is closer to 27
Therefore, 6/22 to the nearest whole number is 27%.
Hopefully this helps!
Answer: 27%
Step-by-step explanation:
Given the fraction [tex]\frac{6}{22}[/tex], you need to divide the numerator by the denominator in order to rewrite it as a decimal number.
[tex]\frac{6}{22}=0.27[/tex]
Now, to express it in percentage, the final step is to multiply the decimal number by 100.
Therefore, you get that [tex]\frac{6}{22}[/tex] to the nearest whole percent is:
[tex](0.27)(100)=27\%[/tex]
Find x Round to the nearest tenth
Answer:
15.5
Step-by-step explanation:
So the formula here is the square of the tangent length is equal to the product of the exterior part of the secant line and total length of the secant.
So that means we have x^2=10(14+10).
After simplifying the right hand side we have the equation is x^2=10(24) or x^2=240.
To get rid of the square on the x, we square root both sides.
x=sqrt(240)
x=15.49193338
To the nearest tenths, the answer is x=15.5
So 15.5 inches is the length of x.
slope 1/2, passes through (6,4)
Write in slope-intercept form
Answer:
[tex]\large\boxed{y=\dfrac{1}{2}x+1}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{We have:}\ m=\dfrac{1}{2}\ \text{and the point}\ (6,\ 4).\\\\\text{The equation:}\ y=\dfrac{1}{2}x+b.\\\\\text{Put the coordinates of the point to the equation:}\\\\4=\dfrac{1}{2}(6)+b\\\\4=3+b\qquad\text{subtract 3 from both sides}\\\\1=b\to b=1\\\\\text{Finally:}\\\\y=\dfrac{1}{2}x+1[/tex]
your utility bill for april is $170. If you pay after the due date,a late payment panality of $7.72 is added? what is percent of penality?
Answer:
4.54%
Step-by-step explanation:
Step 1: Write the data
Total bill = $170
Penalty = $7.72
Percentage of penalty = ?
Step 2: Write the formula to find the percentage of penalty
Percentage of penalty = Penalty/Total bill * 100
Percentage of penalty = 7.72/170 * 100
Percentage of penalty = 4.54%
Therefore, the percent of penalty is 4.54%
!!
Find the mode of the following data:
10, 16, 15, 14, 8, 21, 10, 5, 19, 18, 4, 5, 16, 12, 10,9
Answer:
The mode is 10.
Step-by-step explanation:
A mode is basically the number that occurs most in a data set, so first to make it easier you can list the number least to greatest. After that look at the data set and see what number occurs the most. In this situation it is 10 because it occurs 3 times.
In a data set, the mode is the value that appears the most frequently. A set of data can have just one mode, multiple modes, or none at all.
HOW TO SOLVE?To solve mode given series is
[tex]10\\16\\15\\14\\8\\21\\10\\5\\19\\18\\4\\5\\16\\12\\10\\9\\[/tex]
Rearranging series we get
[tex]4\\5\\5\\8\\9\\10\\10\\10\\12\\14\\15\\16\\16\\18\\19\\21\\[/tex]
hence, mode is number with highest frequency which is 10 in this series
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Which expressions have a value of - 1/64 ? Check all that apply.
Answer:
That may be one of the answers but it is check all that apply
Step-by-step explanation:
Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon.
TYSM
Answer:
Area of the polygon = 59 in²
Explanation:
From the given diagram, we can note that the given polygon is composed of an upper triangle, a side triangle and a rectangle
Therefore:
Area of polygon =
area of upper triangle + area of side triangle + area of rectangle
1- getting the area of the upper triangle:
We have:
base of triangle = 7 in
height of triangle = 6 in
Therefore:
Area of upper triangle = [tex]\frac{1}{2}*base*height = \frac{1}{2}*7*6=21[/tex] in²
2- getting the area of the side triangle:
We have:
base of triangle = 4 in
height of triangle = 5 in
Therefore:
Area of upper triangle = [tex]\frac{1}{2}*base*height = \frac{1}{2}*4*5=10[/tex] in²
3- getting the area of the rectangle:
We have:
length of rectangle = 7 in
width of rectangle = 4 in
Therefore:
Area of rectangle = length x width = 7 x 4 = 28 in²
4- getting the total area of the polygon:
Area of polygon =
area of upper triangle + area of side triangle + area of rectangle
Therefore:
Area of polygon = 21 + 10 + 28 = 59 in²
Hope this helps :)
Answer ASAP John is thinking of a number. He gives the following 3 clues. ``My number has 125 as a factor. My number is a multiple of 30. My number is between 800 and 2000.'' What is John's number?
Answer:
1500
Step-by-step explanation:
List of multiples of 125 between 800 and 2000: 875,1000,1125,1250,1375,1500,1625,1750,1875,2000
Of those only 1500 is divisible by 30: 1500 / 30 = 50
The john number should be 1,500,
Calculation of number:The List of multiples of 125 that lies between 800 and 2000 should be 875,1000,1125,1250,1375,1500,1625,1750,1875,2000
Here we can see that there is only 1500 that should be the multiple of 30
Therefore, the john number should be 1500
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a cruise ship has a rectangular swimming pool.The width of the pool is 30% of the length of the pool.the perimeter of the pool is 1040 feet.what is the width of the pool?What is the length of the pool?
Answer:
The length of the pool is 400 feet.
The width of the pool is 120 feet.
Step-by-step explanation:
We are given the width (W) is 30% of the length (L).
We are also given the perimeter of the pool is 1040.
So in equation form this is what we have:
W=.3L (of means multiply)
2L+2W=1040
We are going to plug the first equation into the second like so:
2L+2(.3L)=1040
2L+.6L=1040
2.6L=1040
Divide both sides by 2.6
L=1040/2.6
L=400
The length of the pool is 400 feet.
W=.3L
W=.3(400)
W=120
The width of the pool is 120 feet.
We get two equations that we can use for this equation.
2w + 2L = 1040
and
w = 0.3L
We can input w into the first equation:
0.6L + 2L = 1040
2.6L = 1040
L= 400
W = 120
Vince bought 6 boxes of worms to use as
bait while fishing with his friends. If each
person uses exactly 3/8 of a box of worms,
how many people can share the worms?
Which of the following is an example of a conditional probability?
O
A. The probability that a volcano will erupt tomorrow.
O
B. The probability that a person will not fall while skating.
O
C. The probability a person will ace a test given that the person got a
good night's sleep the previous night.
O
D. The probability that a road will be closed or a certain song will
come on the radio.
Answer:
The probability a person will ace a test given that the person got a
good night's sleep the previous night.
Step-by-step explanation:
A conditional probability is a probability that something will occur given that something else has happened.
C The probability a person will ace a test given that the person got a
good night's sleep the previous night.
are alternate interior angles always congruent
Answer:
depends
Step-by-step explanation:
The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
Answer:
Yes they are
Step-by-step explanation:
when a line cuts two parallel lines, the alternate interiors angles are congruent. Hope this helps :)
Which of the following shapes is the cross-section for a cylinder?
The cross-section of a cylinder is in the shape of a Circle
Cross section for a cylinder is circle in shape.
What is cross section?" Cross section is defined as the intersection of the solid body with a plane along it particular axis."
According to the question,
Given shape,
Cylinder
Cylinder is having a circular base.
Intersection of a plane with the cylinder is circular.
Cross section of cylinder is circle.
Hence, Option(C) is the correct answer.
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Which functions have a vertex with a x-value of O?. Select three options.
f(x) = |x|
f(x) = \x{ + 3
f(x) = 5x + 31
f(x) = [x] - 6
f(x) = 5x + 31 - 6
Answer:
Step-by-step explanation:
1) f(x) = |x| has its vertex at (0, 0), so the x-value is 0.
2) Cannot figure out what you meant by \x{ + 3.
3) f(x) = 5x + 31 has a straight line graph, no vertex.
4) [x] - 6 does not have a vertex, or at least not a well-defined one like |x|
5) Unsure of what you meant by 5x + 31 - 6. Did you mean 5x + 25? This does not have a vertex.
if f(x)=3x^2-9 and g(x)=x^2+1 find (f+g)(x)
Answer:
4x^2 -8
Step-by-step explanation:
f(x)=3x^2-9
g(x)=x^2+1
(f+g)(x)=3x^2-9 +x^2+1
Combine like terms
= 4x^2 -8
If f(x) = 3x^2
and g(x) = x+2, find (f•g)(x).
A. 3x3 +6x
B. 3x2 +6x
c. xi +2
D. 3x3 +6x2
Answer:
D. (f · g)(x) = 3x³ + 6x²Step-by-step explanation:
(f · g)(x) = f(x) · g(x)
We have f(x) = 3x² and g(x) = x + 2. Substitute:
(f · g)(x) = (3x²) · (x + 2) use the distributive property
(f · g)(x) = (3x²)(x) + (3x²)(2)
(f · g)(x) = 3x³ + 6x²
Jermiah makes a recipe that calls for 1 1/2 cups of flour and 3/4 stick of butter. If Jermiah uses 3 sticks of butter, how many cups of flour will he need
Answer:
The answer is 6 cups of flour.
To find the amount of flour needed for 3 sticks of butter, a proportion based on the original recipe ratio is used, resulting in 6 cups of flour.
Jermiah's recipe calls for 1 1/2 cups of flour for every 3/4 stick of butter. Therefore, if he uses 3 sticks of butter, we need to find out how many cups of flour that corresponds to.
To determine the amount of flour needed, we set up a proportion, where the original amount of butter and flour are proportional to the new amount of butter and flour.
Since 3/4 stick of butter corresponds to 1 1/2 cups of flour, 3 sticks of butter would be 4 times as much, because 3 divided by 3/4 equals 4. Therefore, he will need 4 times the original amount of flour.
Here is the math: 1 1/2 cups of flour x 4 = 6 cups of flour.
Given 0 below, if GH and JK are congruent, what is the measure of KOJ?
Answer:
D
Step-by-step explanation:
Since GH and JK are congruent then the central angles are congruent, that is
∠KOJ = ∠HOG = 68° → D
The measure of KOJ = 68 degree.
What is a sector ?A sector is formed by two radii and the intercepted arc on the circle.
The angle subtended by the sector at the center is called Central Angle.
It is given that the
sector , GH and JK are congruent.
As they are congruent the angle subtended by them at the center will be equal.
The measure of ∠GOH = 68 degree
∠KOJ = ∠GOH = 68 degree
Therefore , The measure of KOJ = 68 degree.
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