Answers
Since in both given equations, the variable y is already clear, then you can equal the two equations and then solve for x. So, you have
[tex]\begin{cases}y=x^2+5x-10\text{ (1)} \\ y=-x^{2}+2x+10\text{ (2)}\end{cases}[/tex][tex]\begin{gathered} x^2+5x-10=-x^2+2x+10 \\ \text{ Add }x^2\text{ to both sides of the equation} \\ \text{ Subtract 2x to both sides of the equation} \\ \text{ Subtract 10 to both sides of the equation} \\ x^2+5x-10+x^2-2x-10=-x^2+2x+10+x^2-2x-10 \\ 2x^2+3x-20=0 \end{gathered}[/tex]To solve for x you can use the quadratic formula, that is,
[tex]\begin{gathered} \text{ For }ax^2+bx+c=0\text{ where a}\ne0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]In this case
a=2
b=3
c=-20
So,
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{(3)^2-4(2)(-20)}}{2\cdot2} \\ x=\frac{-3\pm\sqrt[]{9+160}}{4} \\ x=\frac{-3\pm\sqrt[]{169}}{4} \\ x=\frac{-3\pm13}{4} \\ x_1=\frac{-3+13}{4}=\frac{10}{4}=\frac{5}{2}=2.5 \\ x_2=\frac{-3-13}{4}=\frac{-16}{4}=-4 \end{gathered}[/tex]Now you can plug in the solutions found in any of the given equations to find their respective y-coordinates.
For the first solution, you have
[tex]\begin{gathered} x_1=\frac{5}{2} \\ y_{}=-x^2+2x+10\text{ (2)} \\ y_1=-(\frac{5}{2})^2+2(\frac{5}{2})+10 \\ y_1=-\frac{25}{4}+5+10 \\ y_1=\frac{35}{4} \\ y_1=8.75 \\ \text{ Then} \\ (2.5,8.75) \end{gathered}[/tex]For the second solution, you have
[tex]\begin{gathered} x_2=-4 \\ y=-x^2+2x+10\text{ (2)} \\ y_2=-(-4)^2+2(-4)+10 \\ y_2=-16-8+10 \\ y_2=-14 \\ \text{Then} \\ (-4,-14) \end{gathered}[/tex]Therefore, the solution set of the given system of equations is
[tex]\mleft\lbrace(-4,-14),(2.5,8.75)\mright\rbrace[/tex]Related Questions
Solve triangles using the law of cosines . Find BC
Answers
The cosine rule states that:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]For the given triangle:
a= BC
b=AC=12
c=AB=9
∠A=87º
Replace the known measures on the formula:
[tex]BC^2=12^2+9^2-2(9\cdot12\cdot\cos 87)[/tex]Solve the exponents and the multiplication on the last term:
[tex]\begin{gathered} BC^2=144+81-216\cos 87 \\ BC^2=213.695 \end{gathered}[/tex]-Apply the square root to both sides of the expression:
[tex]\begin{gathered} \sqrt[]{BC^2}=\sqrt[]{213.695} \\ BC=14.618 \\ BC\approx14.62 \end{gathered}[/tex]The length of side BC is 14.62units
Evaluate the following expression given.
Answers
In order to evalute this function, we must substitute x=-2 into the equation. It yields
[tex]\frac{4(-2)+3(-2)+2(-2)+(-2)}{-2}[/tex]By computing the porduct we have
[tex]\frac{-8-6-4-2}{-2}[/tex]which is equat to
[tex]\begin{gathered} \frac{-20}{-2} \\ \sin ce\text{ minus times minus is plus, we have} \\ \frac{10}{2} \end{gathered}[/tex]Finally, the evaluations gives 5.
Red Ribbon Week starts Friday. If the average smoker pays $8.25 for packof cigarettes and smokes 1.5 P(packs per day). Using the equationC=8.25PT, determine how much does that smoker spend on cigaretteseach day? Each week? Each 30 day month? Each 365 day year? (T is theamount of time in days)
Answers
You have the next equation:
[tex]c=8,25PT[/tex]Data: P=1.5
How much does that smoker spend on cigarettes:
Each day: As T is amunt of time in days, to find how much that smoker spend on cigarettes in one day you: Sustitute the T by 1 in the equation:
T=1day
[tex]c=8,25(1.5)(1)[/tex][tex]c=12.375[/tex]Each day the smoker spends $12.375Each week: A week have 7 days
T=7days
[tex]c=8,25(1.5)(7)[/tex][tex]c=86.625[/tex]Each week the smoker spends $86.625Each 30 day month:
T=30 days
[tex]c=8.25(1.5)(30)[/tex][tex]c=371.25[/tex]Each 30 day month the smoker spends $371.25Each 365 day year:
T=365 days
[tex]c=8.25(1.5)(365)[/tex][tex]c=4516.875[/tex]Each 365 day year the smoker spends $4516.875
A small car has a tire with a 15-inch diameter. A mountain bike has a tire with a 27-inch diameter. How much father than the small car does the mountain bike have to drive for its tire to complete one revolution?
Answers
Answer:
The mountain bike will travel 37.7 inches farther than the small car in one complete revolution.
[tex]37.7\text{ inches}[/tex]Explanation:
The distance a tire travel in one complete revolution is equal to the circumference of the tire.
The circumference can be calculated using the formula;
[tex]C=2\pi r=\pi d[/tex]Where;
C = Circumference
r = radius of tire
d = diameter of the tire
For the small car with tire of diameter 15 inches, the distance travelled in one revolution is;
[tex]\begin{gathered} C_1=\pi d_1=\pi(15)=15\pi \\ C_1=47.12\text{ inches} \end{gathered}[/tex]For the mountain bike with tire of diameter 27 inches, the distance travelled in one revolution is;
[tex]\begin{gathered} C_2=\pi d_2=\pi(27)=27\pi_{} \\ C_2=84.82\text{ inches} \end{gathered}[/tex]The difference between the distance travelled in one complete revolution is;
[tex]\begin{gathered} \Delta C=C_2-C_1=84.82-47.12 \\ \Delta C=37.70\text{ inches} \end{gathered}[/tex]Therefore, the mountain bike will travel 37.7 inches farther than the small car in one complete revolution.
[tex]37.7\text{ inches}[/tex]match the angle measurements in radians with equilateral measurements less than or equal to 360°
Answers
The first thing we have to know is that pi= 180º
[tex]\begin{gathered} \frac{23\pi}{4}=\frac{23(180º)}{4}=1035 \\ \end{gathered}[/tex]From this value of 1035 we must subtract 360 for each turn of the circumference until it gives us a value less than 360
[tex]\begin{gathered} 1035-360=675 \\ 675-360=315º \end{gathered}[/tex]So the first answer would be
[tex]\frac{23\pi}{4}\to315º[/tex]Using the same methodology the following angles would give
[tex]\begin{gathered} \frac{18\pi}{5}_{}\to288º \\ \frac{22\pi}{9}\to80º \\ \frac{19\pi}{3}_{}\to60º \end{gathered}[/tex]Solve the equation. Round your answer to the nearest hundredth.-4 = -1.5j + 3+ 32
Answers
Given the equation :
-4 = -1.5 j+ 32
combine like terms
-4 - 32 = -1.5 j
-36 = -1.5j
OR can be written
-1.5 j = -36
Divide both sides by -1.5
[tex]j=\frac{-36}{-1.5}=\frac{36}{1.5}=\frac{36\cdot10}{1.5\cdot10}=\frac{360}{15}=24[/tex]so, the value of j = 24
evaluate and express answer in standard form.
4.56×3.6
________
0.12
Answers
The value of the given expression in the standard form is 1.368×10².
We are given a mathematical expression. The expression consists of two arithmetic operations. First of all, two numbers are multiplied by each other, and then their result is divided by the third number. Let the mathematical expression be denoted by the variable "E". The expression is given below.
E = (4.56×3.6)/0.12
First, we will multiply the numbers in the numerator.
E = 16.416/0.12
Now we will divide the numerator by the denominator.
E = 136.8
Hence, the value of the expression is 136.8. Now we need to convert the resulting number into standard form. The standard form is given below.
E = 1.368×10²
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Anna has four more nickels than dimes in her pocket for a totalof $1.25. Which equation could be used to determine the numberof dimes, x, in her pocket?A$0.05(x + 4) + $0.10x = $1.25B $0.05(4x) + $0.10x + $1.25C$0.05x + $0.10(x + 4) = $1.25D$0.05x + $0.10(4x) = $1.251 point
Answers
Let 'x' be the amount of nickels Anna has, and 'y' the amount of dimes.
If she has '4 more nickels than dimes' this is:
[tex]y=x+4[/tex]And the total amount is $1.25, that can be written as:
[tex]0.05\cdot x+0.10\cdot y=1.25[/tex]If we replace the equivalence between y and x here we get:
[tex]0.05x+0.10(x+4)=1.25[/tex]The correct answer is option C
Hi! I need some help with this question!I am pretty sure my answer is correct , but I just need to check in overall and review the question!Thank you!
Answers
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
Verify each table
Remember that
In a proportional relationship, the linear equation passes through the origin (0,0)
we have that
Am B and C passes through the origin
so
I will check table D
we have the points
(10,30) and (15,45)
Find the slope
m=(45-30)/(15-10)
m=15/5
m=3
Find the equation in slope intercept form
y=mx+b
we have
m=3
point (10,30)
substitute
30=3(10)+b
b=0
y=3x
Verify with this equation for the other points
For x=100
y=3(100)=300 ----> is ok
For x=200
y=3(200)=600 ----> is ok
that means
table D is proportional
Verify table C
we have
(0,0) and (1,3)
m=(3-0)/(1-0)
m=3
Find the equation in slope intercept form
y=mx+b
we have
m=3
point (0,0)
y=3x
Verify the other points
For x=2
y=2(3)=6
6 is not equal to 9
that means
table C is not proportiona
answer is C
Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3
Answers
The required three options accurately represent the statement are options b, c, and e.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
According to the question,
A negative 3 less than 4.9 times a number, x, is the same as 12.8.
12.8 = 4.9x -(-3)
which matched with options b, c, and e.
Thus, the required three options that accurately represent the statement are options b, c, and e.
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Circle 1 is centered at (-4, -6) and has a radius of 9 centimeters. Circle 2 is centered at (4, 2) and has a radius of 6 centimeters. What is the scale factor?Which translation rule will translate Circle 1 to Circle 2?
Answers
For this type of problem we first notice that the center of the first circle has coordinates (-4,-6) and the center of the second one has coordinates (4,2) then all point of circle 1 (x,y) are translated according to the rule (x+8,y+8).
For the scale factor, we notice that the radius of circle 1 is 9 cm and the radius of circle 2 is 6cm then the scale factor is (2/3).
Determine whether each linear relationship is a direct variation. If so, state the constant of proportionality. (Example 4) 4. Pictures, x 3 4 5 6 51 Minutes, 185 235 285 335 Profit, y 24 32 40 48 Cost, y 60 100 140 180 7. 6. Game, X 2 5 20 5 15 10 Year, x Polnts, y 4 1 5 6 7 25 50 12.5 37.5 Helght, y
Answers
table 4 . Direct Variation, constant of proportionality =8
Table 5: No. There is not a direct variation, for the growth is not at a constant factor.
1) To state whether there is a direct variation, we need to examine each row to stat how it increases or decreases
2) So for table 4
x y
3 24
4 32
5 40
6 48
For this, we can write a linear function y=8x
Yes. Direct Variation. Constant of proportionality 8
Table 5
x y
185 60
235 100
285 140
335 180
No. There is not a direct variation, for the growth is not at a constant factor.
Table 6
x y
5 12.5
10 25
15 37.5
20 50
We can set a linear function for that y=5/2 x
Yes. Direct Variation. Constant of proportionality 5/2 (2.5)
Table 7
x y
2 4
3 5
4 6
5 7
There is not a direct variation, for the growth is not at a constant factor.
1. Name one of the segments shown2.calculate their midpoint and lengths(as decimal rounded to the nearest tenth)3.identify all parallel segments
Answers
For naming a segment, we have to know its extrem points. If those extreme points are A and B, we name the segment as:
[tex]\bar{AB}[/tex]We are going to take as an example the segment with extreme points I and C, shown at the left above part of the image, so its name will be:
[tex]\bar{IC}[/tex]Find the reference angle for 342°. 1) 35°2) 5°3) 18°4) 162°
Answers
For an angle a in the fourth quadrant, the reference angle is given by:
360º - a
The angles in the fourth quadrant are those between 270º and 360º. So, 342º is in the fourth quadrant, and its reference angle is:
360º - 342º = 18º
Therefore, the third option is correct.
-8.2d + 28.1 = 3.6d is the solution Positive or Negative?
Answers
The given expression : -8.2d + 28.1 = 3.6d
Simplify the expression for the d :
-8.2d + 28.1 = 3.6d
Subtract 3.6d on both side of the equation
-8.2d -3.6d + 28.1 = 3.6d -3/6d
-11.8d + 28.1 = 0
Subtract 28.1 on both side :
-11.8d + 28.1 - 28.1 = -28.1
-11.8d = -28.1
Multiply both side by ( -1)
(-1) ( -11.8d) = (-1)(-28.1)
11.8d = 28.1
Divide both side by 11.8
11.8d/11.8 = 28.1/11.8
d = 2.38
Answer : d = 2.38
Ten less than a number cubed is negative seven
Answers
We have
less than means subtract from
number cubed means elevate a number to power 3
therefore
Ten less than a number cubed is negative seven
is
[tex]x^3-10=-7[/tex]
The figure below shows a circular lawn.Its diameter is 72 ft.72 ftftft?2(a) Use the calculator to find the area and circumference of the lawn.Use 3.14 for T in your calculations, and do not round your answers,Make sure to include the correct units.?AreaCircumference: 0(b) The lawn will be surrounded by tape.Which measure would be used in finding the amount of tape needed?Circumference AreaCheck2021 McGraw. Educatio ARON
Answers
We are given a circle with a diameter of 72 ft. We are asked to determine its area. To do that we will use the following formula:
[tex]A=\frac{\pi D^2}{4}[/tex]Where "D" is the diameter. Replacing the values:
[tex]A=\frac{(3.14)(72ft)^2}{4}[/tex]Solving the operations:
[tex]A=4069.44ft^2[/tex]Now we are asked to determine the circumference of the circle, to do that we use the following formula:
[tex]C=\pi D[/tex]Replacing the values:
[tex]C=(3.14)(72ft)[/tex]Solving the operations:
[tex]C=226.08ft[/tex]Since the circumference is the measure of the longitude of the circle, if it were to be surrounded by tape this is the measure we would have to use.
bea earned $ 11,700.00 commission for selling a house calculated at 6/100 of the selling price. what was the selling price of the house?
Answers
Given:
Commision earned = $11,700
The commission was calculated at 6/100 of the selling price.
To find the selling price of the house, we have the equation:
[tex]11700=\frac{6}{100}S[/tex]Where S represents the selling price of the house.
Let's solve for S.
Multiply both sides of the equation by 100:
[tex]\begin{gathered} 11700(100)=\frac{6}{100}S\ast100 \\ \\ 1170000=6S \end{gathered}[/tex]Divide both sides of the equation by 6:
[tex]\begin{gathered} \frac{1170000}{6}=\frac{6S}{6} \\ \\ 195000=S \\ \\ S=195000 \end{gathered}[/tex]Therefore, the selling price of the house is $195,000
ANSWER:
$195,000
The image represents a Biased Sample Population Sample. true or false
Answers
ANSWER:
True
STEP-BY-STEP EXPLANATION:
The sample is said to be biased when there is a difference between the sample data and the data for the entire population.
In this case, the sample and the population have different values, which means that the sample does have bias.
Given f(x)=x^3+kx+5f(x)=x
3
+kx+5, and x+1x+1 is a factor of f(x)f(x), then what is the value of kk?
Answers
The value of k associated to the cubic equation f(x) = x³ + k · x + 5 is equal to - 6.
What is the value of k of a cubic equation?
In this question we have a cubic equation of the form f(x) = x³ + k · x + 5 and we need to determine the value of k such that the binomial x + 1 is a factor of f(x). A value of x is a factor of the polynomial if and only if the following expression is observed:
f(x) = 0, for x = a
If we know that x = 1 and f(1) = 0, then the value of k is:
1³ + k · 1 + 5 = 0
k + 6 = 0
k = - 6
The cubic equation has a value of k equal to - 6.
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true or false? if a line is horizontal, there is no x-intercept
Answers
The Solution:
Given that a line is horizontal.
We are asked to determine whether it is true or false that the line has no x-intercept.
Clearly, horizontal lines do not hintercept with x-axis.
Therefore, there is certainly no x-intercept.
Thus, the correct answer is [TRUE]
An engineer has designed a value that will regulate water pressure on an automobile engine. The valve was tested on 120 engines and the mean pressure was 4.6 pounds/square inch. Assume the variance is known to be 0.64. If The valve was designed to produce a mean pressure of 4.4 pounds/square inch, is there sufficient evidence at the 0.1 level that the Valve performs above the specifications? State the null and alternative hypothesis for the above scenario
Answers
The valve was designed to produce a mean pressure of 4.4, this means that our null hypothesis has to be:
[tex]H_0:\mu=4.4[/tex]Since we want to determine if there is sufficient evidence that the valve is aboce the specifications, this means that we want to determine if the mean is greater than 4.4, that is, the alternartive hypothesis is:
[tex]H_a:\mu>4.4[/tex]how can u do 3725 x 28
Answers
What is the area of sector GHJ, given that θ= π/3 radians? Express your answer in terms of π and as a decimal rounded to the nearest tenth.
Answers
Answer:
[tex]\text{area of sector=4.7 square }\imaginaryI\text{nches}[/tex]Step-by-step explanation:
The area of a sector when the angle is measured in radians is represented by:
[tex]\text{ area of sector= }\frac{1}{2}r^2\theta[/tex]The given theta is pi/3, and the radius is 3 inches.
[tex]\begin{gathered} \text{ area of sector=}\frac{1}{2}*3^2*\frac{\pi}{3} \\ \text{ area of sector=}\frac{3}{2}\pi \\ \text{ Convert as a decimal rounded to the nearest tenth:} \\ \text{ area of sector= 4.7 square inches} \end{gathered}[/tex]Three consecutive even integers of which the largest is 2n
Answers
Integers are whole numbers. They are either positive or negative
Even numbers are numbers that are completely divisible by 2 without a remainder.
Even numbers could be 2, 4, 6, 8, 10. the list goes on
If 2n is the largest even integer in the given sequence, then the lesser consecutive even integers would be
2n - 2
2n - 2 - 2 = 2n - 4
Three consecutive even integers of which the largest is 2n are
2n - 4, 2n - 2, 2n
Write the mixed number as an improper fraction. 2 8/9
Answers
Draw an angle in standard position inQuadrant I that has legs of 6 inches and 8inches.
Answers
Given:
There is an angle lying in quadrant II that has legs of 6 inches and 8 inches
The drawing of the angle will be as follows:
As shown in the figure the angle x lying in the quadrant II
And the legs of the right-angle triangle = 6 inches and 8 inches
Note: the legs can be reversed, which gives us another possible solution.
In a survey of 52 pet owners, 26 said they own a dog, and 14 said they own a cat. 13 said they own botha dog and a cat? How many owned a dog but not a cat?
Answers
From the given data we know that
[tex]26[/tex]owners own a dog, but out of those,
[tex]13[/tex]own both a cat and a dog.
Therefore, the number of pet owners that own only a dog is
[tex]26-13.[/tex]Answer:
[tex]13.[/tex]after swimming 80 ft below the surface of the water a whale swims of 40 ft using a number line to help you create an equation that shows the location of the well and relation to the water surface
Answers
We have a whale that swims 80 ft below the surface and then goes up 40 ft.
We can describe her trajectory from surface (y=0) to 80 ft below (y=-80) and then 40 ft up (y=-80+40=-40).
The correct interpretation is Option D: the equation is -80+40=-40. The whale is 40 ft below the surface.
I need help with Number 5 please tell me what to put in the box
Answers
The price of a pair of tires is $130.56. We want to know the price of ten tires. Ten tires, is the same as five pairs of tires, then, since we know the price of a pair the price of five pairs will be just five times the price of the pair.
The price of five pairs is:
[tex]5\times130.56=652.80[/tex]$652.80.