Answers
We have then:
x ^ 2 + 10x + 12 = 36
Rewriting:
x ^ 2 + 10x-24 = 0
The roots for this case are:
x1 = 2
x2 = -12
Answer:
The roots of the polynomial are:
x1 = 2
x2 = -12
Related Questions
Given: a quadrilateral with sides of 12 yards, 14 yards, 16 yards, and 18 yards. On a drawing, 1 inch = 2 yards, how long are the sides of the quadrilateral on the drawing?
A. 6,7,8 and 9 inches
B. 24,28,32 and 36 inches
C. 60, 70, 80 and 90 inches
Answers
[tex] \frac{12}{2} \: \: \: \frac{14}{2} \: \: \: \frac{16}{2} \: \: \: \frac{18}{2} \: \: \: \\ 6 \: \: \: \: \: 7 \: \: \: \: \: 8 \: \: \: \: \: 9[/tex]
so A is true
Answer:
The correct answer is option A, 6 , 7, 8, 9 inches
Step-by-step explanation:
Given the scale of drawing ,
[tex]1 inch = 2 yards\\[/tex]
The size of each side of a quadrilateral when converted as per the scale pf map
[tex]= \frac{12}{2} , \frac{14}{2} , \frac{16}{2} , \frac{18}{2} \\= 6, 7, 8 , 9 inches\\[/tex]
A pool in the shape of s rectangle has a perimeter 80 feet. The pool is 8 feet less wide than it is long
Answers
44 for length and 36 for width
The shorter leg of a 30-60-90 triangle is 4. How long is the hypotenuse?
Answers
Therefore it is 8
In a 30-60-90 triangle, the hypotenuse is twice the length of the shortest leg. Hence, if the shortest leg is 4, then the hypotenuse is 8.
Explanation:In a 30-60-90 triangle, the ratios of the sides are specific and constant. The shortest side, the one opposite the 30-degree angle, is considered to be x. The longest side (hypotenuse), directly across from the 90-degree angle, is 2x, and the remaining side is x√3. In this case, the shortest side (x) is indicated to be 4.
So, in this triangle, the hypotenuse (2x) would be 2*4 = 8.
The Pythagorean theorem, as mentioned in the reference content, will also hold, but in the case of this special triangle, the ratios of the sides simplify the process of determining side lengths.
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what expression represents a number t increased by 10
Answers
t+10
in a pile of coins there are 7 more quarters than nickels if there is a total of $2.65 in coins how many quarters are there guess check and revise to solve
Answers
A quarter is worth $0.25 and a nickle is worth $0.05. Suppose the number of quarters is represented by q and the number of nickels is represented by n.
First Equation
"There are 7 more quarters than nickels" could be written as
⇒ q = n + 7
Second Equation
"There is a total of $2.65" could be written as
⇒ 0.25q + 0.05n = 2.65 (change to whole number, multiply both side by 100)
⇒ 25q + 5n = 265
Work on the system of equation
Substitute q = n + 7 to the second equation
25q + 5n = 265
25(n + 7) + 5n = 265
25n + 175 + 5n = 265
30n + 175 = 265
30n = 265 - 175
30n = 90
n = 90/30
n = 3
The number of nickels is 3
Substitute n = 3 to the first equation
q = n + 7
q = 3 + 7
q = 10
The number of quarters is 10
helpppppppppppppppppppppp
Answers
7x (x^2 * y)^1/3 which is the last option
Explanation:
5x (x^2 * y)^1/3 + 2 (x^5 * y)^1/3
5x (x^2/3 * y^1/3) + 2 (x^5/3 * y^1/3)
5 * x^5/3 * y^1/3 + 2 * x^5/3 * y^1/3
(5+2) * x^5/3 * y^1/3
7* x^5/3 * y^1/3
which can be rewritten as:
7x (x^2 * y)^1/3 which is the last option
Hope this helps :)
Find X. This is Big Ideas Geometry Chapter 9.3
Answers
You can set up a ratio with the largest triangle to the second largest.
30/50=x/40
50x=1200 x=24 units
The value of x of the triangle is: x = 24 units
How to find the length of similar triangles?Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
Thus, the length of the base is:
c² = 30² + 40²
c² = 2500
c = √2500
c = 50 units
Using the concept of similarity ratio, we have:
30/50 = x/40
Cross multiply to get:
50x = 1200
x = 24 units
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Find the balance in the account after the given period. $3500 deposit 6.75% compounded monthly, after 6 months
Answers
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$3500\\ r=rate\to 6.75\%\to \frac{6.75}{100}\to &0.0675\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to \frac{6}{12}\to &\frac{1}{2} \end{cases} \\\\\\ A=3500\left(1+\frac{0.0675}{12}\right)^{12\cdot \frac{1}{2}}\implies A=3500(1.005625)^6[/tex]
Which statement about BC←→ is correct?
BC←→ is a tangent line because △ABC is a right triangle.
BC←→ is a tangent line because the sum of the angles in △ABC is 180º.
BC←→ is not a tangent line because m∠ABC≠90°.
BC←→ is a tangent line because m∠ABC is acute.
Answers
So a tangent line is perpendicular to the radius, which means it creates a 90 degree angle with the radius of the circle. The sum of the interior angles of any triangle is 180 degrees. To determine if line BC is a tangent line, we have to determine if angle ABC is 90 degrees. Well we know the degrees of the other two angles of the triangle, so let's set up an equation:
180 = 48 + 47 + x
180 = 95 + x
85 = x
Since angle ABC must be 85 degrees (not 90), line BC is not a tangent line.
Answer:
BC←→ is not a tangent line because m∠ABC ≠ 90°.
The measure of angle at the tangent of a circle is a right angle.
The correct statement about BC is (c) BC is not a tangent line because m∠ABC≠90°.Start by calculating the measure of angle ABC using the following angle in a triangle theorem
[tex]\angle ABC + 48 + 47 = 180[/tex]
[tex]\angle ABC + 95 = 180[/tex]
Subtract 95 from both sides of the equation
[tex]\angle ABC = 180 - 95[/tex]
[tex]\angle ABC = 85[/tex]
For line BC to be a tangent, then the following must be true
[tex]\angle ABC = 90[/tex]
Hence, the correct statement about BC is (c)
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If you add 0.43 to a certain number then subtract 0.58 from the result and then another 4.04, you’ll get 30.3. What is the certain number?
Please show how you did it.
Answers
(((0.43+x)-.58)-4.04) = 30.3
(0.43+x)-4.64 = 30.3
x-4.21 = 30.3
x = 30.3 + 4.21
x = 34.51
The answer is 34.51 and there's the work for you. Have a great day!
Answer:
34.49
Step-by-step explanation:
You do it reverse
30.3+4.04=34.34
34.34+0.58=34.92
34.92-0.43=34.49
the radius of a circular park is 120 m. to nearest meter, what is the circumference of the park.
Answers
A=πr²
2 x 3.14 x 120 = 754
Does the interest rate increase at a constant rate?
6 months = 2.4%
9 months = 2.9%
12 months = 3.0%
18 months = 3.1%
Answers
From 6 mo to 12 mo, it increases 0.6%.
From 12 mo to 18 mo, it increases 0.1%. The change over a 6 mo period gets smaller as the period gets longer or the rate gets higher.
it seems what's being asked is, "is the change from a month to the next, constant", as in an arithmetic sequence, well, check the picture below, those coordinates do not give us a straight line, and therefore, we don't have an arithmetic sequence, and therefore, we don't have a "common difference".
and since we don't have a common difference, the rate is not constant.
3 less than the quotient of a number y and 4
Answers
Quotient ⇒ division
The required algebraic expression can be written as [tex](y\div4)-3[/tex].
Given: a statement is [tex]3[/tex] less than the quotient of a number [tex]y[/tex] and [tex]4[/tex].
According to question,
An algebraic expression can be written by use of [tex]3[/tex] less than the quotient of a number [tex]y[/tex] and [tex]4[/tex].
Here, expression is [tex](y\div4)-3=\frac{y}{4}-3[/tex].
Therefore, the algebraic expression for the statement [tex]3[/tex] less than the quotient of a number [tex]y[/tex] and [tex]4[/tex] is written as [tex]\frac{y}{4}-3[/tex].
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Jane plans to invest $500 at 8.25% interest, compounded continuously. After 14 years, how much money has she accumulated? Has her money doubled or tripled?
Answers
After 14 years, Jane has accumulated approximately $1587.45, which means her initial investment of $500 has more than tripled due to the power of compound interest at a rate of 8.25%, compounded continuously.
Jane plans to invest $500 at 8.25% interest, compounded continuously. To find out how much money she has accumulated after 14 years, we use the formula for continuous compounding: [tex]A = Pe^{rt}[/tex], where:
For Jane's investment:
P = $500
r = 8.25% or 0.0825 (as a decimal)
t = 14 years
Plugging these values into the formula gets us:
[tex]A = 500e^{0.0825*14}[/tex]
Calculating this gives us:
[tex]A \approx 500e^{1.155} \approx 500 * 3.1749 \approx $1587.45[/tex]
Jane's money has more than tripled in 14 years. It has not quadrupled, but it has significantly grown beyond double the original investment.
Erick, Mia, and Isabelle golfed 9 holes. Erick scored 10 more than Mia, and Isabelle scored 16 less than twice Mia's score. Use the drop-down menus to complete the statements about the expression that represents the scenario. What does the expression x + x + 10 + 2x – 16 represent from the given scenario? What does the variable in the expression represent? What is the expression in simplified form? What is the constant in the simplified expression?
Answers
Answer:
1. The total score of all three players.
2. Mia's score.
3. 4x-6\
4. -6
The mathematical expression from the scenario represents the total golf scores of Erick, Mia, and Isabelle. The variable represents Mia's score, and the simplified expression is 4x - 6, with -6 being the constant.
Explanation:From the given scenario, the expression x + x + 10 + 2x - 16 represents the total score of Erick, Mia, and Isabelle. The variable 'x' in this expression represents Mia's golf score, as other scores are dependent on it.
To simplify the expression, we group like terms: x (Mia's score) + x (Erick's score, which is 10 more than Mia's) + 2x (Isabelle's score, which is 16 less than twice Mia's) - 16. Simplifying this, we get 4x - 6. So, the simplified expression is 4x - 6.
The constant in the simplified expression is -6. This is the value that is added or subtracted to the variable's value, irrespective of its value.
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Use the grouping method to factor the polynomial below completely.
2x3 + 16x2 + 7x + 56
A. (x2 + 8)(x + 7)
B. (x2 + 7)(x + 8)
C. (2x2 + 7)(x + 8)
D. (2x2 + 8)(x + 7)
Answers
Which is C. (2x2+7)(x+8)
Hope I helped! :)
Leyla drops a penny from a height of 150 m.
How long will it take the penny to hit the ground?
Use the formula h(t)=−4.9t2+vot+h o, where vo is the initial velocity and h o is the initial height. Round to the nearest tenth of a second.
Answers
Answer:
I believe its 5.5
Step-by-step explanation:
WILL GIVE A BRAINLEST !!!!
The graph of a logarithmic function is shown below.
What is the domain of the function?
x < 0
x > 0
x < 1
all real numbers
Answers
Hope this helps!
Answer: The correct option is second, i.e., x>0.
Explanation:
As we know that the domain is the set of all possible inputs. If function is defined as, f(x) then all possible value of x for which the function f(x) is defined is called domain.
In a graph the domain is defined on the x axis and the range of the function is defined on y-axis.
In the given graph the function is defined from x=0 to [tex]x=\infty[/tex] because for [tex]x\leq 0[/tex] the graph is not defined. It means for [tex]x\leq 0[/tex] the function is not defined.
Sicen the graph is defined for all positive values of x, therefore the domain of the function is al real number greater than 0. It can be written as x>0 and the second option is correct.
What transformation has changed the parent function f(x) = 3(2)x to its new appearance shown in the graph below?
exponential graph passing through point 0, 5.
f(x) + 2
f(x) + 4
f(x + 2)
f(x + 4)
Answers
f (x) = 3 * (2) ^ x
Then, we have the following fact that is a fact of the problem:
"exponential graph passing through point 0, 5"
Thus,
Original graphic:
f (x) = 3 * (2) ^ x
f (0) = 3 * (2) ^ 0
f (0) = 3
Graph with transformation:
g (x) = 3 * (2) ^ x + 2
g (0) = 3 * (2) ^ 0 + 2
g (0) = 3 + 2
g (0) = 5
Go through the point (0, 5)
Therefore the graph is:
g (x) = 3 * (2) ^ x + 2
g (x) = f (x) + 2
answer:
f (x) + 2
Find the area of circle B in terms of π.
Answers
Answer:
(2.25π) yd²
Step-by-step explanation:
The area of a circle is given by the formula:
[tex]\boxed{\text{Area of circle}=\pi r^{2} }[/tex] , where r is the radius.
In this question, the radius is 1.5 yd.
Substitute r= 1.5 into the formula:
Area of circle B
[tex]=\pi (1.5)^2[/tex]
= (2.25π) yd²
Additional:
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https://brainly.com/question/15245049The ratio of the segments into which the altitude to the hypotenuse of a right triangle divides the hypotenuse is 9 : 4. what is the length of the altitude? 6 36 3 cannot be determined
Answers
√(4*9) : 4 : 9 = 6 : 4 : 9
Since these are ratios, not measures, the actual length of the altitude cannot be determined. (4th selection)
Which of the following best describes the intersection of two planes? (Points : 5)
line
line segment
point <
ray
I think its Point?
Answers
What is the slope of a line parallel to line B?
Answers
Answer:
[tex]\frac{5}{2}[/tex]
Step-by-step explanation:
The slope of a line parallel to b has the exact same slope as b. Therefore, by finding the slope of b, you will find the slope of a line parallel to be as well.
The following formula is used to find m, the slope of the line, using the two given points:
[tex]m=\frac{y_{1}-y_{2} }{x_{1}-x_{2} } \\m=\frac{5--5}{3--1} \\m=\frac{5+5}{3+1} \\m=\frac{10}{4} \\m=\frac{5}{2}[/tex]
Write the equation of the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0.
Answers
x + 2y + 4 =0
Explanation:
1) You know a point (4 - 1) and that the line is perpendicular to a given line.
2) From the equation of the perpendicular line whose equation was given, you determine the slope, for which you can use the slope-intercept form of the equation:
2x - y - 7 = 0 => y = 2x + 7.
The slope is the coeffiicient of x, which is 2.
Therefore, slope = 2.
3) The slope of the other line is the negative inverse of the slope of the perpedicular line:
slope = - 1/2
4) Now that you have the slope of your line and the point (4, - 1) you determine the equation with this procedure:
y - b
------- = slope
x - a
where a y b are the coordinates of the point (4, - 1) and the slope is -1/2
=>
y - (-1)
---------- = - 1/2
x - 4
5) Simplify
2(y + 1) = - (x - 4)
2y + 1 = - x + 4
2y + x +1 + 4 = 0
x + 2y + 4 =0 <---------- this is the equation searched.
Which values are solutions to the inequality below? Check all that apply [tex] \sqrt{x} [/tex]>13
a) 26
b) 28560
c) 15
d) 170
e)1
f)251
Answers
question 1
Solve the system of equations and choose the correct answer from the list of options.
d + e = 15
−d + e = −5
Label the ordered pair as (d, e).
A (0, 0)
B (10, −5)
C (5, 10)
D (10, 5)
question2
A set of equations is given below:
Equation S: y = x + 9
Equation T: y = 2x + 1
Which of the following steps can be used to find the solution to the set of equations?
A x = 2x + 1
B x + 9 = 2x
C x + 1 = 2x + 9
D x + 9 = 2x + 1
Question 3
A set of equations is given below:
Equation C: y = 6x + 9
Equation D: y = 6x + 2
Which of the following options is true about the solution to the given set of equations?
A One solution
B No solution
C Two solutions
D Infinite solutions
question 4
Solve the system of equations and choose the correct answer from the list of options.
2x + y = −4
y = 3x + 2
A negative 6 over five comma negative 8 over 5
B negative 8 over 5 comma negative 6 over 5
C negative 5 over 6 comma negative 11 over 5
D negative 11 over 5 comma negative 6 over 5
question 5
A system of equations is given below:
y = –2x + 1
6x + 2y = 22
Which of the following steps could be used to solve by substitution?
A 6x + 2(−2x + 1) = 22
B −2x + 1 = 6x + 2y
C 6(−2x + 1) + 2y = 22
D 6(y = −2x + 1)
Answers
2. d
3. b
4. a
5. a
those are the answers to the questions
Answer:
1.D
2.D
3.B
4.A
5.A
Step-by-step explanation:
1.We are given that two equations
[tex]d+e=15[/tex]
[tex]-d+e=-5[/tex]
Adding two equations then we get
[tex]2 e=10[/tex]
[tex]e=\frac{10}{2}=5[/tex]
Substitute e=5 in equation one then we get
[tex]5+e=15[/tex]
[tex] d=15-5[/tex]
[tex]d=10[/tex]
Hence, the ordered pair as (10, 5).
Therefore,Option D is true.
2.We are given that two equations
Equation S:[tex]y=x+9[/tex]
Equatin T:[tex]y=2x+1[/tex]
Using substitution method
Substitute the value of y from equation one in equation second then we get
[tex]x+9=2x+1[/tex]
Therefore, option D is true.
3.We are given that two equations
Equation C :[tex]y=6x+9[/tex]
Equation D[tex]:y=6x+2[/tex]
The two equations can be written as
[tex]6x-y+9=0[/tex]
[tex]6x-y+2=0[/tex]
[tex]a_1=6,b_1=-1,c_1=9[/tex]
[tex]a_2=6,b_2=-1,c_2=2[/tex]
[tex]\frac{a_1}{a_2}=\frac{6}{6}=1:1[/tex]
[tex]\frac{b_1}{b_2}=\frac{-1}{-1}=1:1[/tex]
[tex]\frac{c_1}{c_2}=\frac{9}{2}[/tex]
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}[/tex]
Therefore, system of equations have no solution
Hence, option B is true.
4.We are given that two equations
[tex]2x+y=-4[/tex]
[tex]y=3x+2[/tex]
Using substitution method
Substitute value of y from equation second in equation one
Then we get
[tex]2x+3x=2=-4[/tex]
[tex]5 x=-4-2[/tex]
[tex]5 x=-6[/tex]
[tex]x=-\frac{6}{5}[/tex]
Substitute the value of x in equation second then we get
[tex]y=3\times( -\frac{6}{5})+2[/tex]
[tex]y=\frac{-18+10}{5}[/tex]
[tex]y=-\frac{8}{5}[/tex]
Hence, option A is true.
5.We are given that two equations
[tex]y=-2x+1[/tex]
[tex]6x+2y=22[/tex]
Using substitution method
Substitute value of y from equation one in second equation then we get
[tex]6x+2(-2x+1)=22[/tex]
Hence, option A is true.
Jen has 12 ounces milkshake. 4 ounces in the milkshake are vanilla, and the rest is chocolate. What are two equivalent fractions that represent the fractions of the milkshake that is vanilla?
Answers
There are two parts two a fraction. The top part is called the numerator, which shows how many of the parts indicated by the denominator are taken.
The bottom part is called the denominator, which is the total amount of that particular thing.
In this case, 12 would be the denominator and the and 4 would be the numerator. Your fraction would look like:
4/12
Now, this question asks for equivalent fractions. An equivalent fraction is a fraction that is equivalent to the first fraction.
To equivalent fractions could be:
2/6 and 1/3
How I got these fractions? I simply divided the numerator and denominator by 2, and then again by 2 to get 1/3.
Good Day!
Which two equations would be most appropriately solved by using the zero product property? Select each correct answer. 4x² = 13 0.25x2+0.8x−8=0 −(x−1)(x+9)=0 3x2−6x=0
Answers
Answer:
−(x−1)(x+9)=0
And..
3x2−6x=0
Step-by-step explanation:
Final answer:
The two equations most appropriately solved by using the zero product property are −(x−1)(x+9)=0 and 3x²−6x=0, as they can be directly factored into a product of terms equaling zero.
Explanation:
The question involves finding which two equations would be most appropriately solved by using the zero product property. The zero product property states that if the product of two numbers is zero, then at least one of the multiplicands must be zero. Therefore, equations that can be factored into a product of terms equaling zero can be solved using this property.
−(x−1)(x+9)=0: This equation is already in a factored form and directly applies the zero product property. Set each factor equal to zero and solve for x: x−1=0 or x+9=0, which gives x = 1 or x = −9.3x²−6x=0: This equation can be factored as 3x(x−2)=0. By applying the zero product property, set 3x=0 and x−2=0, solving for x gives x = 0 or x = 2.The other options, 4x² = 13 and 0.25x²+0.8x−8=0, are not immediately in a form that uses the zero product property without further manipulation or do not directly apply to this property.
Find the values of sand y
VR=y
TS=x+11
VT=y-3x
RS=x+2
Answers
therefore, y=x+11 and x+2=y-3x
y=x+11 , 2=y-4x
y=x+11 , y=4x+2
then use the process of elimination:
y=4x+2 then plug in: y=3+11
- y=x+11 y=14
0=3x-9 I think this is how you'd do it, tbh it's just an educated
3x=9 , x=3 guess. Btw, sorry if it looks weird
helpppppppppppppppppppppppppppppppp
Answers
(1 / x) = ((x + 3) / (2x ^ 2))
(2x) = (x + 3)
Then we clear x:
(2x) = (x + 3)
2x-x = 3
x = 3
Answer:
x = 3
option 4