Solve the simultaneous equations
y = 4x-2
y = 4x² - 9x + 3
Give your answers correct to 2 decimal places.
Answers
Answer:
The answer is in the pictures.
Step-by-step explanation:
Related Questions
I NEED HELP ASAP
Solve.
4x + 2(3x – 9) = x
A.
x = –2
B.
x = 1.8
C.
x = 2
D.
x = 18
Answers
Answer:
x=2
Step-by-step explanation:
\(4x+2(3x-9)=x\\\\\implies 4x +6x - 18 -x =0\\\\\implies 9x = 18\\\\\implies x = \dfrac{18}9 = 2\)
What is the least five-digit even number with no repeated digits?
Answers
Use pic for more info
Answers
Answer: The answer is D
Step-by-step explanation: Hope that this helps.
Given: The coordinates of rhombus WXYZ are W(0, 4b), X(2a, 0), Y(0, -4b), and Z(-2a, 0).
Prove: The segments joining the midpoints of a rhombus form a rectangle.
As part of the proof, find the midpoint of YZ.
Answers
The midpoint of segment YZ is (-a, -2b).
Given the coordinates of the rhombus WXYZ:
W(0, 4b)
X(2a, 0)
Y(0, -4b)
Z(-2a, 0)
Find the midpoint of YZ:The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Substituting the coordinates of Y and Z:
Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)
= (-a, -2b)
Therefore, the midpoint of segment YZ is (-a, -2b).
Show that the segments joining the midpoints are perpendicular:To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.
Let's consider the segments joining the midpoints:
Segment joining the midpoints of WX and YZ:
Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)
Midpoint of YZ: (-a, -2b)
Slope of WX = (2b - 4b) / (a - 0) = -2b / a
Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a
The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.
Conclusion:We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.
Additionally, the midpoint of segment YZ is (-a, -2b).
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Factor each polynomial. Look for a GCF first.
2x²-8k-90
O
2 (x-9) (x - 5)
2 (x + 9) (x + 5)
2 (x − 9) (x + 5)
2 (x + 9) (x - 5)
Answers
Answer:
Step-by-step explanation:
First, you could factor 2 out of the whole thing. The result would be 2(x^2-4x-45). Now we find the factors of 45 which are 1, 45, 5, 9, 15, 3. We have to find the pair that adds up to 4, and multiply to get 45. After some guess and check, we can find that 5 and 9 are those numbers. Now we have to get the right signs. Since the result is a negative number for -8k, and -90, the number that is a negative must be less than the other negative. -9<-5, so the answer would be 2(x-9)(x+5)
if the vertex of an angle is on the edge of a circle
Answers
Answer:
When we say an angle is on a circle, we mean the vertex is on the edge of the circle. One type of angle on a circle is the inscribed angle (see Inscribed Angles in Circles). Another type of angle on a circle is one formed by a tangent and a chord.
A projectile is fired straight up from ground level. After t seconds, its height above the ground is s feet, where s= - 161? + 112t. For what time period is the projectile at least 160 feet above the ground?
Answers
The time period the projectile at least 160 feet above the ground is 2 sec to 5sec.
What is time period?
The duration of time that a behavior lasts or a condition persists. Depending on the type of activity or situation under consideration, it may be measured in seconds or in millions of years.
Given function that represents height of the projectile above the ground is s feet is s = - 16t² + 112t.
To find the time period is the projectile at least 160 feet above the ground, make an inequality:
- 16t² + 112t ≥ 160
Subtract 160 from both sides:
- 16t² + 112t - 160 ≥ 0
Divide both sides by 16:
- t² + 7t - 10 ≥ 0
- t² + 2t + 5t - 10 ≥ 0
-t(t -2) + 5(t - 2) ≥ 0
(t - 2)( -t+ 5) ≥ 0
Either, t - 2 ≥ 0 → t ≥ 2
or, -t + 5 ≥ 0 → t ≤ 5
2 ≤ t ≤ 5
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What is the value of x in the equation?
2/3 (x + 6) = -18
Answers
Help Now Important
4(x−2+y)=
Answers
I hoped this helped you for math
Answer:
4(x-2 +y) = 4x-8+4y
Step-by-step explanation:
You have to apply the distributive law
4(x-2+y) = 4x + 4 (-2) + 4y
Then solve it which equals
4 x +4 (-2) + 4y
Then multiply the numbers
4 (-2) = -8
Which gets you 4x-8+4y
A principal of $2900 is invested at 6% interest, compounded annually. How much will the investment be worth after 11 years?
Use the calculator provided and round your answer to the nearest dollar.
Answers
Answer:
$5,505
Step-by-step explanation:
Compound interest formula :
A = P (1 + r/n)^(nt)Solving after substituting the given values :
A = (2,900)(1 + 0.06/1)¹¹A = (2,900)(1.06)¹¹A = (2,900)(1.89829856)A = $5,505 (nearest dollar)Solve the matrix
x+y-z=3
2x+3y+z=10
3x-y-7z=1
Answers
A = [1 1 -1
2 3 1
3 -1 -7]
X = [x
y
z]
B = [3
10
1]
We can use matrix elimination or Gaussian elimination to solve for X:
Step 1: Subtract 2 times the first row from the second row:
A = [1 1 -1
0 -1 3
3 -1 -7]
B = [3
4
1]
Step 2: Subtract 3 times the first row from the third row:
A = [1 1 -1
0 -1 3
0 -4 -20]
B = [3
4
-8]
Step 3: Divide the second row by -1:
A = [1 1 -1
0 1 -3
0 -4 -20]
B = [3
-4
-8]
Step 4: Subtract the second row from the third row:
A = [1 1 -1
0 1 -3
0 0 -16]
B = [3
-4
-12]
Step 5: Divide the third row by -16:
A = [1 1 -1
0 1 -3
0 0 1]
B = [3
-4
12/16]
Step 6: Subtract -3 times the second row from the first row:
A = [1 0 4
0 1 -3
0 0 1]
B = [15/4
-4
12/16]
Step 7: Solve for x by multiplying the first row by 4:
A = [1 0 4
0 1 -3
0 0 1]
B = [3
-4
12/16]
X = [3
-4
3/4]
So the solution to the system of linear equations is X = [3, -4, 3/4].
Divide.
5÷1/4
1/20
4/5
5/4
20
Answers
Answer:
20.
Step-by-step explanation:
That's the correct answer
Answer:
20
Step-by-step explanation:
To divide by a fraction, such as 1/4, we invert the fraction and then multiply instead of dividing. Thus:
5÷1/4 = 5*(4/1) =20
jason went shopping.
he bought a watch and a pair of trainers for a total price of £53.55
this price includes a 15% loyalty discount.
before the discount the trainers were priced at £38.
work out the price before the discount.
Answers
Answer:
The total price before discount was £63.
The price of the watch before discount was £25.
Step-by-step explanation:
Let the total original price before discount be x.
The total of £53.55 included a 15% discount. That means he paid only 85% of the original total price before the discount.
85% of x = £53.55
0.85x = 53.55
x = 63
The total before discount was £63.
£63 - £38 = £25
The total price before discount was £63.
The price of the watch before discount was £25.
I need help with this please explain.
Answers
The area of this figure is,
⇒ 103.5 in²
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
The figure is made with three figures triangle, two rectangles.
Since, Area of triangle = 1/2 × Length × Breadth
Hence, We get;
Area of triangle = 1/2 × 5 × 3
Area of triangle = 7.5 in²
And, Area of rectangle = Lenght × Width
For large rectangle;
⇒ Length = 9 in.
⇒ Width = 8 in.
Thus, We get;
Area of rectangle = Lenght × Width
Area of rectangle = 9 × 8
Area of rectangle = 72 in²
And, For small rectangle;
Length = 4 in
Width = 6 in.
Thus, We get;
Area of rectangle = Lenght × Width
Area of rectangle = 4 × 6
Area of rectangle = 24 in²
Therefore, The area of this figure is,
⇒ 7.5 + 72 + 24 in²
⇒ 103.5 in²
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s/4 +5=13
How do i solve thissssssss
Answers
\(\dfrac{s}{4} +5=13\)
Simplify:
\(\dfrac{1}{4} s+5=13\)
Subtract 5 from both sides:
\(\dfrac{1}{4} s+5-5=13-5\)
\(\dfrac{1}{4} s=8\)
Multiply both sides by 4:
\(4\times(\dfrac{1}{4} s)=4\times(8)\)
\(\fbox{s = 32}\)
s = 32.
Step-by-step explanation:1. Write the expression.\(\frac{s}{4} +5=13\)
2. Subtract 5 from both sides of the equation.\(\frac{s}{4} +5-5=13-5\\ \\\frac{s}{4} =8\)
3. Multiply by "4" on both sides of the equation.\(\frac{s}{4}*4 =8*4\\ \\s=32\)
4. Verify.If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "s" by it's calculated value, 32.
\(\frac{(32)}{4} +5=13\\ \\8+5=13\\ \\13=13\)
As you can tell, the same number appears on both sides of the equal symbol, this means that the result is correct!
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To play basketball with her friends, Evangeline needs to pump air in her ball, which is completely deflated. Before inflating it, the ball weighs
0.615
0.6150, point, 615 kilograms. Afterwards, it weighs
0.624
0.6240, point, 624 kilograms. The diameter of the ball is
0.24
0.240, point, 24 meters.
Assuming the inflated ball is perfectly spherical, what is the air density within it? Can someone tell me answer please ?
Answers
Answer:
ρ_air = 0.15544 kg/m^3
Step-by-step explanation:
Solution:-
- The deflated ball ( no air ) initially weighs:
m1 = 0.615 kg
- The air is pumped into the ball and weight again. The new reading of the ball's weight is:
m2 = 0.624 kg
- The amount of air ( mass of air ) pumped into the ball can be determined from simple arithmetic between inflated and deflated weights of the ball.
m_air = Δm = m2 - m1
m_air = 0.624 - 0.615
m_air = 0.009 kg
- We are to assume that the inflated ball takes a shape of a perfect sphere with radius r = 0.24 m. The volume of the inflated ( air filled ) ball can be determined using the volume of sphere formula:
V_air = 4*π*r^3 / 3
V_air = 4*π*0.24^3 / 3
V_air = 0.05790 m^3
- The density of air ( ρ_air ) is the ratio of mass of air and the volume occupied by air. Expressed as follows:
ρ_air = m_air / V_air
ρ_air = 0.009 / 0.05790
Answer: ρ_air = 0.15544 kg/m^3
Answer:
1.24
Step-by-step explanation:
Help me please I really need help
Answers
Answer:
it doesn't because it's not a set of ordered pairs
Julie printed out a picture of each of the six members of her favorite band to decorate her bedroom door. Each picture measures 5 inches by 7 inches. Once decorated, how many square inches of Julie's door will be covered by these pictures?
Answers
On Julie's door, the images will span 210 square inches.
As Julie printed six images, the total space that the images cover is:
6 x 35 square inches = 210 square inches
What is an inch?Inches are measured as 1/36 of a yard in both British Imperial and American Customary measurement systems. According to some sources, the term "inch" comes from the Old English "ince" or "ynce," which in turn is said to have originated from the Roman "uncia" unit.
The name of another English unit, the ounce, is derived from the Roman word uncia. According to legend, King David I of Scotland defined the old English word "ynce" as the width of a man's thumb at the base of the nail in the year or thereabouts 1150 AD.
From the question:
Six images total, each measuring 5 by 7 inches, were printed by Julie. We must first calculate the area of each image in order to add up the overall area that these photographs cover.
One image's area is as follows:
5 inches x 7 inches = 35 square inches
As Julie printed six images, the total space that the images cover is:
6 x 35 square inches = 210 square inches
Consequently, 210 square inches of Julie's door will be covered by the images.
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Solve the system of equations by graphing.
y = -2
y = -3
2
x + 4
Answers
The system of graphs is a very unique concept which helps to understand various concepts in a visual way.
How does this occur?
The two lines intersect at (-3, -4), which is the system of equations' solution.
Using the slope and y-intercept, graph an equation as follows:The equation y = mx + b's y-intercept can be found.Determine the y-intercept. The purpose will be (0, b).The slope=m of the equation y = mx + b can be found.Run from the slope while taking a single step using the rise.Your line should join those two spots.This is how the equation can be solved-
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What is the value of the expression n(8n/10) when n =
5?
Answers
Answer:
(8n/10)
8 × 5 = 40
40 ÷ 10 = 4
A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final
answer to four decimal places and intermediate z-value calculations to two decimal places
Answers
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:
0.5874 = 58.74%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).The parameters for this problem are given as follows:
\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)
The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem:
\(Z = \frac{X - \mu}{s}\)
Z = (18.1 - 17.2)/0.3953
Z = 2.28
Z = 2.28 has a p-value of 0.9887.
Z = (17.1 - 17.2)/0.3953
Z = -0.25
Z = -0.25 has a p-value of 0.4013.
Hence:
0.9887 - 0.4013 = 0.5874 = 58.74%.
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if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
\(f(x)=x^{2} +2x-24\)
Answers
(X+6)(x-4)
Hope this helps
yolandaa sunflower is 12 centimeters more than jean sunflower yolanda sunflower is 75 centimeters tall. how tall is jeans sunflower?
Answers
Answer:
63 centimeters
Step-by-step explanation:
Answer: 63 cm tall.
Step-by-step explanation: Yolanda's sunflower is 12 cm more than Jean's sunflower. Yolanda's sunflower is 75cm. To find Jean's sunflower's size in cm simply subtract 12 cm from 75 cm.
75 = 12 = 63
So, Jean's sunflower is 63 centimeters tall.
Please help!!!!
Find the surface area of the composite figure below to
the nearest tenth.
Answers
Answer:
16801.2cm²
Step-by-step explanation:
Cone :
SA = πrl
SA = π · 28 · 45 90-45 = 45
SA = 3958.406744
Cylinder :
SA = 2 · π · r · ( r+h)
SA = 2 · π · 28 ( 28 +45 )
SA = 2 · π · 28 (73)
SA = 12842.83077
12842.83077 + 3958.406744 =
16801.2cm²
2+2995442974346496329869631467646547624672463777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777
Answers
Answer:
2.9954429743464962e+168
Step-by-step explanation:
Which number line shows the solution of 5x - 25 < -15 ? 
Answers
Answer:
The answer is A
The correct number line shown in ''Option A'' is the solution of 5x - 25 < - 15.
What is Number line?Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
We have to given that;
The inequality is,
⇒ 5x - 25 < - 15
Now, We can solve as;
⇒ 5x - 25 < - 15
⇒ 5x < - 15 + 25
⇒ 5x < 10
Divide by 5;
⇒ x < 2
Thus, The solution x < 2 is shown in Option A.
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Let (-3,-2) be a point on the terminal side of theta. Find the csc(theta)
Answers
The csc(theta) = 1/sin(theta) = 1/(-2/√13) = -√13/2. So, the cosecant of theta is -√13/2.
To find the cosecant (csc) of theta when a point (-3, -2) lies on its terminal side, we need to determine the hypotenuse (r) of the right triangle formed by this point.
Using the Pythagorean theorem, r^2 = (-3)^2 + (-2)^2. So, r^2 = 9 + 4 = 13, and r = √13.
The csc(theta) is the reciprocal of sin(theta). Sin(theta) is calculated as the ratio of the opposite side (y-coordinate) to the hypotenuse, or sin(theta) = -2/√13.
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find the value of x 4x + 3 = -5x + 21
Answers
4x + 3 = -5x + 21
9x + 3 = 21
9x = 18
x = 2
Hope this helps!! :)
Answer:
x=2
Step-by-step explanation:
4x + 3 = -5x + 21
add 5x on both sideswhich will get u to 9x +3 = 21subtract 3 from both sideswhich will get u to 9x = 18divide 9 from both sides and the answer is x = 2I am so confused I don't even know which one to choose how to come to the answer
Answers
Answer:
\(y=\frac{1}{9}x-\frac{1}{3}\)Explanation:
The equation of a line in slope-intercept form is given by
\(y=mx+b\)where m = slope and b = y-intercept.
Now in our case, the equation we have is
\(y+\frac{1}{3}=\frac{1}{9}x\)to change it to the slope-intercept form, we have to do some subtraction.
We subtract 1/3 from both sides to get
\(y+\frac{1}{3}-\frac{1}{3}=\frac{1}{9}x-\frac{1}{3}\)the 1 /3 's cancel from the left-hand side, leaving us with
\(\boxed{y=\frac{1}{9}x-\frac{1}{3}}\)Note that the equation above is now in slope-intercept form. The slope, if one is curious, is 1/9 and the y-intercept is - 1/3.
Now, looking at the answer choices given, we see that the option at the very bottom ( the5th choice) matches what we got above. Therefore, the fifth answer choice is the correct option to choose.