[tex]x^2-x-42=0\\x^2+6x-7x-42=0\\x(x+6)-7(x+6)=0\\(x-7)(x+6)=0\\x=7 \vee x=-6[/tex]
Answer:
The roots are 7 and -6.
Keys:
[tex]ax^2+bx+c=0[/tex][tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex][tex]-(-a)^(^n^) = a^(^n^)[/tex][tex]\sqrt[n]{a}^n = a[/tex][tex]1^a = 1[/tex]When you see a ± in a quadratic equation, you will have multiple solutions; more than one.
Step-by-step explanation:
solve the main expression
[tex]x^2-x-42=0\\x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-42\right)}}{2\cdot \:1}\\\rightarrow \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-42\right)}\\=\sqrt{\left(-1\right)^2+4\cdot \:1\cdot \:42}\\\rightarrow \left(-1\right)^2\\=1^2\\=1\\\rightarrow 4\cdot \:1\cdot \:42\\=168\\=\sqrt{1+168}\\=\sqrt{169}\\=\sqrt{13^2}\\=13\\x_{1,\:2}=\frac{-\left(-1\right)\pm \:13}{2\cdot \:1}[/tex]
solve for x₁
[tex]\frac{-\left(-1\right)+13}{2\cdot \:1}\\=\frac{1+13}{2\cdot \:1}\\=\frac{14}{2\cdot \:1}\\=\frac{14}{2}\\=7[/tex]
solve for x₂
[tex]\frac{-\left(-1\right)-13}{2\cdot \:1}\\=\frac{1-13}{2\cdot \:1}\\=\frac{-12}{2\cdot \:1}\\=\frac{-12}{2}\\=-\frac{12}{2}\\=-6[/tex]
Can someone help me answer these
Answer:
1. 05+02=07
07+03=10
2. 05+04=09
09+01=10
3. 05+01=06
06+04=10
4. 05+03=08
08+02=10
5. 17+03=20
6. 19+01=20
Step-by-step explanation:
(Answers are in bold)
if 3 + root8 by 3-root8 + 3-root8 by 3+root8 = a+broot2 find a and b
If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0
What is an equation?An equation is an expression that shows the relationship between two or more variables or numbers.
[tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }\\ \\\frac{9+6\sqrt{8}+8+9-6\sqrt{8}+8 }{(3-\sqrt{8} )(3+\sqrt{8} )} \\\\\frac{34}{9-8} =34+0\sqrt{2}[/tex]
If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0
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Colin borrowed some money at 7.16%/a compounded quarterly. Three years later, he paid $5000 toward the principal and the interest. After another two
he paid another $5000. After another five years, he paid the remainder of the principal and the interest, which totalled $5000. How much money
did he originally borrow?
Based on the calculations below, the amount originally borrowed by Colin is $10,006.67.
How do we calculate the original amount using PV formula?To solve this question, the following present value (PV) formula will be used:
PVn = Pn / (1 + r)^n ........................... (1)
Where:
PVn = Present value of an amount paid in year n
P = Amount paid in year n
r = quarterly interest rate = 7.16% / Number of quarters in a year = 0.0716 / 4 = 0.0179
n = number of quarters = Number of years * Number of quarters in a year = Number of years * 4
Using equation (1), we can therefore proceed as follows:
PV3 = PV of $5,000 paid after three years = $5,000 / (1 + 0.0179)^(3 * 4) = $4,041.18
PV5 = PV of $5,000 paid after another 2 years (after 3 years + 2 years = 5) = $5,000 / (1 + 0.0179)^(5 * 4) = $3,506.45
PV10 = PV of $5,000 paid after another 5 years (after 3 years + 2 years + 5 years = 10) = $5,000 / (1 + 0.0179)^(10 * 4) = $2,459.04
Therefore, we have:
Original amount borrowed = PV3 + PV5 + PV10 = $4,041.18 + $3,506.45 + $2,459.04 = $10,006.67
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A cyclist cycles a distance of 36 miles in a time of 3 hours.
What is her average speed?
Answer:
12mph
Explanation:
Is cos²α the same thing as cosα²?
Answer:
No, it is not the same thing.
Step-by-step explanation:
Hope this helps!
What is the solution set for 2|3y+7|=10
Answer:
[tex]y = \frac{7}{2} [/tex]
Step-by-step explanation:
[tex]3y + 7 = 5y \\ 7 = 5y - 3y \\ 7 = 2y \\ \frac{7}{2} = y \\ y = \frac{7}{2} [/tex]
Reflect the shape A in the line y
=
y
(-5, 6)
(4,3)
(-3, 1)
-8-7 -6 -5 -4 -3 -2 -1
4 5 6 7 8
-1
-2
-3
-4
-5
-6
-7
-8
What are the coordinates of the vertices
of the image?
A
00
8
7
6
LO
5
4
3
2
-
1
Đ
1
-2
3
-X.
2
(-5,6)
Step-by-step explanation:
2.) x/2 = 1 Solving equations.
Answer: x=2
Step-by-step explanation:
To find the value of x, we have [tex]\frac{x}{2} =1[/tex]. To isolate x, we want to multiply both sides by 2 to get x alone.
x=2
Answer:
2
Step-by-step explanation:
[tex] \frac{x}{2} = 1 \\ cross \: multiplying \\ x = 2 \times 1 = 2 \\ x = 2[/tex]
Solve the quadratic equation 5x^2+x+1=0
Answer:
No Solution
Step-by-step explanation:
Answer:
[tex]x = \dfrac{-1\pm i\sqrt{19}}{10}[/tex]
Step-by-step explanation:
[tex]~~~~~~5x^2 +x +1 = 0\\\\\implies x = \dfrac{-1\pm\sqrt{1^2 -4 (5)(1)}}{2(5)}\\\\\implies x = \dfrac{-1 \pm \sqrt{-19}}{10}\\\\\implies x = \dfrac{-1\pm i\sqrt{19}}{10}[/tex]
which type of statement has the form' "if A, then B"
Answer:
list statements please or I cannot help you.
Step-by-step explanation:
or do you want me to make a statement?
Answer: Conditional Statement
A conditional is of the form "if, then" which is often found in math classes and formal logic classes as well.
simplify -x(4x^2 − 6x + 1)
Answer:
[tex]-4x^3+6x^2-x[/tex]
Step-by-step explanation:
1. Distribute the X across the equation: [tex]-x(4x^2)=-4x^3\\[/tex]
2.[tex]-x(-6x)=6x^2[/tex]
3.[tex]-x(1)=-x[/tex]
3.[tex]-4x^3+6x^2-x[/tex]
(giving 100 points) What is the equation of the line of best fit for the following data? Round the slope and y-intercept of the line to three decimal places.
x y
4 3
6 4
8 9
11 12
13 17
A: y = 1.560x - 4.105
B: y = -4.105x + 1.560
C: y = 4.105x - 1.560
D: y = -1.560x + 4.105
please hurry
Answer:
Slope-intercept form of a linear equation: [tex]y=mx+b[/tex]
where:
[tex]m[/tex] is the slope[tex]b[/tex] is the y-interceptTo determine the equation of the line of best fit from the given answer options, examine the relationship between the x and y values.
From inspection of the data, we can see that as x increases, y increases. Therefore, the slope of the equation will be positive.
(If the y-values decrease as the x-values increase, then the slope would be negative).
Therefore, we can immediately discount answer options B and D as they have negative slopes.
The x and y values are not very far away from each other. The options given for the slope are either 1.560 or 4.105. If the slope was 4.105, we would expect to see values of y that were further away from the x-values.
Therefore, the line of best fit is:
A: y = 1.560x - 4.105
To prove this, plot the 5 points on a graph and draw a line of best fit (see attached).
Choose 2 points on the line of best fit: (4, 2) and (11, 13)
Use the slope formula with these points to calculate the approximate slope:
[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}\approx\dfrac{13-2}{11-4}=\dfrac{11}{7}=1.57[/tex]
Thus proving that y = 1.560x - 4.105 is an appropriate option for the equation of the line of best fit.
The local school board needs to choose whether to build an addition to the elementary school library or remodel the high school basketball court. Which sampling option might the board choose to survey the community?
Why is it important to avoid a smaller sample size?
Answer:
Don't know the full answer, though I searched it up on brainly and found this:
Hopefully it can help you with whatever you are doing/taking.
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Anybody!!!!!! Select all that equals to 6(4)(6(-5))
Answer:
[tex]\frac{1}{6}[/tex]
[tex]6^{-1}[/tex]
[tex]\frac{1}{6^{1} }[/tex]
Step-by-step explanation:
Answer:
[tex]\frac{1}{6}[/tex] and [tex]6^{-1}[/tex] also [tex]}{\frac{1}{6^{1} } }[/tex] which is the same as [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
According to exponent rules
[tex]a^{n} *a^{m} =a^{n+m}[/tex]
[tex]a^{-x}= \frac{1}{a^{x} }[/tex]
Please answer quickly!!
Answer:
B is true
C is false
D is false
Step-by-step explanation:
- B is true because two negative numbers are added together, the outcome is negative hence always less than 0
- C is false due to needing a negative number add to -1.5 to be less, a positive only makes the number greater
- D is false since you are adding 0.9 (9/10), anything less than this will m ake the sum be greater than 0
example: - 0.5 + 0.9 = 0.4 or - 0.8 + 0.9 = 0.1
Question 3 of 10
10 Points
Write an equation in slope-intercept form of the line that passes through the point
(3,-2) with slope -2.
A.y=-2-2(x-3)
B. y = -2x + 4
Oc.y+2=-2(x-3)
OD. 2x+y-4 = 0
Reset Selection
The equation in slope-intercept form of the line that passes through the point is y = -2x+4 , Option B is the correct answer.
What is the equation of a straight Line ?The equation of a straight line is given by the equation
y= mx+c
Where m is the slope and
c is the intercept on y axis.
The given data is
line passes through the point (3,-2) with slope -2.
m = -2
y = -2x + c
-2 = - 2 * 3 +c
-2 = -6 +c
c = +4
y = -2x+4
Therefore Option B is the correct answer.
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find the distance between the two points in simplest radical form.
(3,-8) and (8,4)
Answer:
13
Step-by-step explanation:
The way to find the distance between two points on the coordinate plane is to use the distance formula, which is basically a way of applying the Pythagorean Theorem.
The distance formula is [tex]\sqrt{(x_{1}- x_{2} )^2 + (y_{1}- y_{2})^2}[/tex]. Let's say the coordinate (3, -8) is (x1, y1) and the coordinate (8, 4) is (x2, y2). We can plug these values into the formula:
[tex]\sqrt{(3- 8 )^2 + (-8 - 4)^2}\\\sqrt{(-5)^{2} + (-12)^{2}} \\\sqrt{25+144} \\\sqrt{169} \\13[/tex]
So, the distance between the two points is 13.
What is the length of AC in the given triangle?
Answer: the answer is 126.6
Step-by-step explanation:
Answer:
AC ≈ 126.6
Step-by-step explanation:
The law of sines can be used to find the side length of interest in this triangle. It tells you ...
a/sin(A) = b/sin(B) = c/sin(C)
__
missing angleIn order to use the law of sines, we must have a side length and its opposite angle. Here, the angle opposite the given side is unmarked, so we need to compute it using the angle sum theorem.
A +B +C = 180°
A +85° +53° = 180°
A = 42° . . . . . . . . . . . . . subtract (85°+53°)
unknown sideThen side AC can be found from ...
AC/sin(B) = BC/sin(A)
AC = BC·sin(B)/sin(A) = 85·sin(85°)/sin(42°)
AC ≈ 126.547
The closest answer choice is 126.6.
A recent survey of people who eat salad suggest that 78% like tomatoes on their salad, 49% like cheese on their salad, and 36% like both tomatoes and cheese on their salad. suppose a person who eats salad is selected at random, and find they like cheese on their salad. what is the probability that the person also likes tomatoes on their salad? 0.29 0.46 0.49 0.73
By definition of conditional probability, the probability that the person also likes tomatoes on their salad is 0.73 or 73% (last option).
Definition of probabilityProbability is the greater or lesser possibility that a certain event will occur.
In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.
Definition of conditional probabilityThe conditional probability P(A|B) is the probability that an event A occurs, knowing that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. Is defined as:
P(A|B) = P(A∩B)÷ P(B)
Probability that the person also likes tomatoes on their saladIn this case, you know:
Event A: Person likes tomatoes on their salad.Event B: Person likes cheese on their salad.Being the event A∩B (A intersection B) when A and B occur simultaneously, then:
P(A)= 78%=0.78P(B)= 49%= 0.49P(A∩B)= 36%=0.36Suppose a person who eats salad is randomly selected and likes cheese on his salad, the probability that the person also likes tomatoes on their salad is:
P(B|A) = P(A∩B)÷ P(B)
Then:
P(A|B) = 0.36÷0.49
P(B|A) = 0.73= 73%
Finally, the probability that the person also likes tomatoes on their salad is 0.73 or 73% (last option).
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fractions and decimals
(just the simplest fractions, but if i did anything wrong on the greatest common factor, correct that please & thank you)
Answer:
All the GCFs look good! Here's the simplified fractions:
Step-by-step explanation:
1. 2/3
2. 3/4
3. 3/7
4. 3/16
5. 27/29
6. 4/11
7. 2/11
Simply divide the numerator by the GCF to find the simplified numerator, and the denominator by that same GCF to find the simplified denominator!
The volume of this cone is 3,183.96 cubic meters. What is the height of this cone?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
height = 18m
Step-by-step explanation:
cone volume = 3183.96 m³
1/3 πr²h = 3183.96
1/3×3.14×13×13×h = 3183.96
h = 3183.96×3/13×13×3.14
h = 9551.88/530.66
h = 18
1/3x + 1/4y = 1
2x – 3y = –30
Answer:
(-3, 8) is the solution
Step-by-step explanation:
The LCD of the first equation is (3)(4) = 12. Rewriting this equation, we get:
4x + 3y = 12
to which we add the second equation, obtaining:
4x + 3y = 12
2x - 3y = -30
-------------------
6x = -18
Dividing both sides by 6 yields x = -3
Substituting -3 for x in the first equation yields 4(-3) + 3y = 12, or
-12 + 3y = 12
Then 3y = 24 and y must be 8.
The solution to this system of linear equations is (-3, 8).
Simplify: 4^2+√9 what is the answer
[tex]~~4^2 +\sqrt 9\\\\=16 +3 \\\\=19[/tex]
Help me please I beg lol I can’t solve it (step by step in comments)
Answer:
272 m
Step-by-step explanation:
You have to devide the shape in 2.
Complete the steps to find the surface area of the right prism shown below.
Steps Example
1. Write the surface area formula. Surface Area = BA + ph
2. Identify the shape of the bases. right
3. Use the correct formula to find the area of one base.
4. Multiply that area by 2 (to get BA, area of both bases). BA = 2 • area of one base
BA = (2)() = units2
5. Find the perimeter of one base. p = 3 + 4 + 5 =
6. Multiply that perimeter by the height of the prism (to get LA, area of all lateral faces). LA = ph = ()(20) = units2
7. Add the results from steps 4 and 6. Surface Area = BA + LA = +
= units2
The surface area of the prism is 144 square units
How to determine the surface area?The attached image represents the missing figure in the question.
The image would be used to complete the steps, as follows:
Step 1: The surface area formula. Surface Area = BA + phStep 2: The shape of the bases are right trianglesStep 3: The area of one base; Area = 0.5 * 3 * 4 = 6Step 4: Multiply the area in (3) by 2: BA = 2 * 6 = 12Step 5: The perimeter of one base. p = 3 + 4 + 5 = 12Step 6: Multiply p by h; LA = 12 * 11 = 132Step 7: Add (4) and (6). Surface Area = 12 + 132 = 144Hence, the surface area of the prism is 144 square units
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Which situation can be represented by the expression -2-5−2−5minus, 2, minus, 5?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The temperature was 222 ^\text{o}\text{C}
o
Cstart superscript, start text, o, end text, end superscript, start text, C, end text and has decreased by 555 ^o\text{C}
o
Cstart superscript, o, end superscript, start text, C, end text.
(Choice B)
B
The temperature was -2−2minus, 2 ^\text{o}\text{C}
o
Cstart superscript, start text, o, end text, end superscript, start text, C, end text and has increased by 555 ^o\text{C}
o
Cstart superscript, o, end superscript, start text, C, end text.
(Choice C)
C
The temperature was -2−2minus, 2 ^\text{o}\text{C}
o
Cstart superscript, start text, o, end text, end superscript, start text, C, end text and has decreased by 555 ^o\text{C}
o
Cstart superscript, o, end superscript, start text, C, end text.
The situation that represents the expression 2 - 5 is (a) the temperature was 2°C and has decreased by 5°C
How to determine the situation?The expression is given as:
2 - 5
When the expression illustrates change in temperature, the interpretation can be:
An initial temperature of 2°C decreases by 5°C
Hence, the situation that represents the expression 2 - 5 is (a) the temperature was 2°C and has decreased by 5°C
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Can somebody help find the surface area if this
The total surface area of the object shown in the diagram is 164 inches.
What is the total surface area?
The total surface area of a 3-dimensional object is the sum of the areas of the faces or surfaces of a 3-dimensional object. The object shown is the net of a cuboid.
Total surface area of a cuboid = 2 (lw + wh + lh)
where:
• l = length
• w = width
• h = height
2 { (10 x 3) + (10 x 4) + (4 x 3)}
2 (30 + 40 + 12)
2 x 82 = 164 inches
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The surface area of the figure is 164 square inches
How to determine the surface area?From the net of the rectangular prism, we have the following dimensions:
Length = 4 inches
Width = 3 inches
Height = 10 inches
The surface area is calculated as:
Area = 2 * (Length * Width + Length * Height + Width * Height)
So, we have:
Area = 2 * (4 * 3 + 4 * 10 + 3 * 10)
Evaluate
Area = 164
Hence, the surface area of the figure is 164 square inches
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Write a differential equation that models the given situation. The stated rate of change is with respect to time t. (Use k for the proportionality constant.) When an advertising campaign for a new product is introduced into a city of fixed population N, the rate of change of the number y of individuals who have heard about the product at time t is proportional to the number of individuals in the population who have not yet heard about the product.
The differential equation that models the given situation will be dy/dt = K(N - y).
How to compute the equation?Let y = number of individuals who have heard about the product.
Let N - y = this who haven't heard about the product.
From the given statement, the rate for change will be t = dy/dt. Therefore, the differential equation that models the given situation will be dy/dt = K(N - y).
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What is the length of segment BC?
Answer:
is there any other info?
How would you write 16,340 in scientific notation with 2 significant figures? 16,300 1.63 x 104 16,000 1.6 x 104
16340 can be written in scientific notation as 1.63 × 10⁴.
What is Scientific Notation?
Scientific Notation is a way of representing large numbers in decimal forms multiplied by the power(exponent) in terms of decimal places. The purpose of representing large numbers in scientific notation is to enable easier calculation.
This means that 16,340 in scientific notation can be expressed as:
= 1.634 × 10⁴
= 1.63 × 10⁴ ( to 2 significant figures)
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