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)
A pool in the shape of s rectangle has a perimeter 80 feet. The pool is 8 feet less wide than it is long
At the start of a race, a runner’s velocity changes from 0 to 4.0 m/s. It takes him 2 seconds to speed up. His acceleration is ______ m/s2.
His acceleration is, 2 m/s^2!
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Choose the pair of numbers that is not a solution to the given equation.
y = 5 - 2x
My options are;
1,3
2,1
0,3
What is the solution set for the quadratic equation x2 - 16 = 0?
A)
{4}
B)
{-4, 4}
C)
{256}
D)
{-256, 256}
Jana wants to navigate page 35 of her report. what is the quickest way to navigate?
To navigate to page 35 of a report, you can use the 'find' function in a web browser with CONTROL or COMMAND + F, utilize the table of contents with hyperlinks, or enter the page number in a navigator window's spin box, depending on the device and format.
To quickly navigate to page 35 of a report, you have several options depending on the format and the device you are using. If you are viewing the report on a web browser, you can usually press CONTROL or COMMAND and the letter F to open the 'find' function and type '35' to jump to page 35. Alternatively, if the document has a table of contents with hyperlinks, you can click on the relevant section to navigate quickly. For documents with a navigator window, enter '35' in the spin box to jump straight to that page. In a mobile reading environment, you may find a Contents button at the top of the screen; clicking this can allow you to select and jump to the desired page or section.
The 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
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.
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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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%
The shorter leg of a 30-60-90 triangle is 4. How long is the hypotenuse?
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 is the derivative of e^(2x)
I am confused because the derivative e^x is e^x.
But they say you need to use the chain rule.
Which is f'(g(x))*g'(x).
I have used that on exponents but in this I just get, 2x * e^(2x-1) *e
Which is not the answer =/
Write the equation of the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0.
What is the slope of a line parallel to line B?
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]
What scale factor was applied to the first rectangle to get the resulting image
Help me plsssssssssssssssssssssssssssssssssssssssssss!
the ordered pairs below represent a relation between x and y.
(-3,0), (-2,4), (-1,8), (0,12), (1,16), (2,20)
could this set of ordered pairs have been generated by a linear function?
A. No, because the distance between consecutive x-value is different than the distance between consecutive x-values.
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
C. No, because the y-values decrease and then increase
D. Yes, because the distance between consecutive x-values is constant.
Answer:
Yes because the relative difference between y-values and x-values is the same no matter what which pairs of (x,y) values you use to calculate it
Step-by-step explanation:
Yes, this set of ordered pairs have been generated by a linear function because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
The correct option is (B)
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given are ordered pairs are: (-3,0) (-2,4)(-1,8)(0,12)(1,16)(2,20).
It can be seen that the there only unit increase in x coordinates and units increase in consecutive y- coordinates.
Now, if we set up the equation of line as:
Here, m =4 and b = 12
So the relationship is linear and represented by the equation
y=4x+12
Hence, the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
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If you were going to represent the top view of the figure, stated which boxed should be shaded.
Find the ordered triple of these equations. 2x - 3y - 4z = -21 -4x + 2y - 3z = -14 -3x - 4y + 2z = -10
Find the area of circle B in terms of π.
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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Solve. 2m^2-7m-13=-10
[tex]2m^2-7m-13=-10\ \ \ |+10\\\\2m^2-7m-3=0[/tex]
[tex]a=2;\ b=-7;\ c=-3\\\\b^2-4ac=(-7)^2-4\cdot2\cdot(-3)=49+24=73\\\\m_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ m_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\m_1=\dfrac{-(-7)-\sqrt{73}}{2\cdot2}=\dfrac{7-\sqrt{73}}{4}\\\\m_2=\dfrac{-(-7)+\sqrt{73}}{2\cdot2}=\dfrac{7+\sqrt{73}}{4}[/tex]
3 less than the quotient of a number y and 4
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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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
What term can you add to 5/6x-4 to make it equivalent to 1/2x-4
Answer:
-1/3
Step-by-step explanation:
We need a c number that:
5/6x + cx = 1/2x
We clear the equation:
cx = 1/2x -5/6x
c = 1/2 -5/6
c= -2/6 = -1/3
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?
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)
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.
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
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.
Find the values of sand y
VR=y
TS=x+11
VT=y-3x
RS=x+2
helpppppppppppppppppppppp
Northbound buses with tourists leave Waco for Dallas at 10 minute intervals. The trip takes exactly one hour. Southbound tourist buses leave Dallas for Waco at the same moment as their northbound counterparts and arrive an hour later. How many southbound buses does a northbound bus encounter between Waco and Dallas, including the one that is arriving in Waco just as the northbound bus leaves for Dallas and the one that is departing from Dallas just as the northbound bus arrives there?
18 points were scored by one figure skating pair that was 40% of your final score. What was the final score for that pair of figure skaters?