The given solutions of the quadratic equation:
x = 4 and x = -1
First we make them factors of the equation:
x= 4 becomes:
[tex]x-4\text{ = 0}[/tex]and x = -1 becomes:
[tex]x\text{ + 1 = 0}[/tex]So (x-4) and (x+1) are the factors.
To get the general quadratic equation, we would expand the factors
[tex]\begin{gathered} (x-4)(x+1)\text{ = 0 } \\ x(x+1)\text{ -4(x+1) = 0} \\ x^2+x\text{ -4x-4 = 0} \end{gathered}[/tex][tex]\begin{gathered} Adding\text{ like terms} \\ x^2-3x-4\text{ = 0} \end{gathered}[/tex]The general quadratic equation:
[tex]x^2\text{ - 3x - 4 = 0}[/tex]Use the “complete the square” method to solve the following problemx^2 + 3x + 11 = 0
[tex]x^2+3x+11=0[/tex][tex](\frac{1}{2}\times3)^2=(+\frac{3}{2})^2[/tex][tex]\begin{gathered} x^2+3x=-11 \\ x^2+3x+(+\frac{3}{2})^2=-11+\frac{9}{4} \\ \\ (x+\frac{3}{2})^2=-\frac{35}{4} \\ \\ x+\frac{3}{2}=\sqrt{\frac{-35}{4}} \\ \\ x+\frac{3}{2}=\pm\frac{\sqrt{35}}{2}i \\ \\ x=\frac{-3}{2}\pm\frac{\sqrt{35}}{2}i \end{gathered}[/tex]
The answers are
[tex]x=\frac{-3}{2}+\frac{i\sqrt{35}}{2},\text{ }x=\frac{-3}{2}-\frac{i\sqrt{35}}{2}[/tex]Solve using elimination.–2x − 7y = 9x − 7y = –15
The question wants us to solve the following system of equations by elimination:
[tex]\begin{gathered} -2x-7=9 \\ x-7y=-15 \end{gathered}[/tex]Solution
[tex]\begin{gathered} -2x-7y=9\text{ (Equation 1)} \\ x-7y=-15\text{ (Equation 2)} \\ \\ \text{Subtract both equations} \\ -2x-7y-(x-7y)=9-(-15) \\ -2x-7y-x+7y=9+15 \\ -2x-x-7y+7y=24 \\ -3x=24 \\ \text{Divide both sides by -3} \\ -\frac{3x}{-3}=\frac{24}{-3} \\ \\ \therefore x=-8 \\ \\ \text{Substitute the value for x into Equation 1}.\text{ This will help us find y.} \\ -2x-7y=9 \\ -2(-8)-7y=9 \\ 16-7y=9 \\ \text{Subtract 16 from both sides} \\ -7y=9-16 \\ -7y=-7 \\ \text{Divide both sides by -7} \\ -\frac{7y}{-7}=-\frac{7}{-7} \\ \\ \therefore y=1 \end{gathered}[/tex]Answer
The answer to the system of equations is:
x = -8
y = 1
A cone has a height of 17 centimeters and a radius of 7 centimeters. What is its volume? Use = 3.14 and round your answer to the nearest hundredth. cubic centimeters
To find the volume of the cone, we will use the formula below:
[tex]V=\frac{1}{3}\pi r^2h[/tex]where r is the radius and h is the height
From the question,
π = 3.14
r =7
h=17
substitute the values into the formula
[tex]V=\frac{1}{3}\times3.14\times7^2\times17[/tex][tex]V\approx871.87\text{ cubic centimeters}[/tex]
Which of the following are maximum and minimum points of the function y = 2 cos x -1?
The graph of the function is shown below
From the options provided
Option A is correct because the maximum and minimum values are satisfied
Which of the following is equivalent to the expression below? (2+31) + (8-21) O A. 6+1 O B. 6+5; O C. 10+57 O D. 10 + 1
Given the expression:
[tex](2+3i)+(8-2i)[/tex]Let's find the equivalent expression from the choices given.
To find the equivalent expression, let simplify.
To simplify the expression, take the following steps:
• Remove the parentheses:
[tex]2+3i+8-2i[/tex]• Combine like terms:
[tex]\begin{gathered} 2+8+3i-2i \\ \\ 10+i \end{gathered}[/tex]Therefore, the equivalent expression is:
[tex]10+i[/tex]ANSWER: D
D. 10 + i
in the diagram the figures are simular, what is x?triangle with 30cm and 13cmtriangle with 24cm and x
If the figures are similar, the proportion between the corresponding sides is the same.
The side of 30 cm corresponds to the side of 24 cm, and the side of 13 cm corresponds to the side of x cm.
So if the proportion is the same, we have that:
[tex]\begin{gathered} \frac{30}{24}=\frac{13}{x} \\ 30\cdot x=24\cdot13 \\ x=\frac{24\cdot13}{30}=\frac{4\cdot13}{5}=\frac{52}{5}=10.4 \end{gathered}[/tex]So the value of x is 10.4 cm, therefore the answer is b.
Fifty people in a room are wearing clothes either in red orwhite or a combination of the two colors. Thirty are wearingonly red and 16 are wearing a combination of both red andwhite. How many are wearing clothes that have white in them?
SOLUTION
We will solve the question using a Venn diagram
Let R represents people wearing clothes that have red
Let W represents people wearing clothes that have white
We have the Venn diagram as follow
So from the Venn diagram small letter w represent those wearing clothes that have only white. So we have that
[tex]\begin{gathered} 30+16+w=50 \\ 46+w=50 \\ w=50-46 \\ w=4 \end{gathered}[/tex]So those for "only" white is 4.
But those wearing clothes that have white in them will be only white plus those wearing combination of red and white. We have
[tex]16+4=20[/tex]Hence the answer is 20
Pyramid with the square base. Is this correct? Base=64in^2LA= 112in^2TA=176in^2
The given figures is of square pryamid with the square base
Area of square = side x side
In the given figure, the length of the base of the square = 8in
Area of base of square = 8 x 8
Area of base of square = 64 in²
The lateral area of a right pyramid can be calculated by
multiplying half of the perimeter of the base by the slant
height.
Lateral surface area = 1/2 x Perimeter of the base x slant height
Since, the base of the pryamid is square so, the perimeter for the base pf pryamid = 4side
Perimeter = 4 x side
Perimeter = 4 x 8
Perimeter of the base of pryamid is 32 in
Slant height is given as 7in
Lateral surface area = 1/2 x 7 x 32
LAteral surface area = 7 x 16
Lateral surface area = 112 in²
The total surface area can be calculated by adding base are to the lateral surface area
Total surface area = Lateral surface area + Base area
Total surface area = 112 + 64
Total surface area = 176 in²
Answer:
Area of base of square = 64 in²
6 eggs weigh 3/4 of a pound. How much does each egg weigh? 1/4 pounds1/6 pounds1/8 pounds2/3 pounds
In order for the parallelogram to be a rhombus, x equals?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
parallelogram diagram
Step 02:
geometry:
solve for x:
(5x + 25)° = (12x + 11)°
5x + 25 = 12x + 11
25 - 11 = 12x - 5x
14 = 7x
14 / 7 = x
2 = x
The answer is:
x = 2
Find f such that the given conditions are satisfied. f(x)=x2-3x + 12, f(0) = 9 O f(x) = 1x2 - 4x² + 12x +9 O O f(x) - x-x2 + 12x + 1 f(x) = 3x3-4x2 + 12x + 1 O f(x) = 3x - x? + 12x + 9
To find f(x) we will do an integration
[tex]\begin{gathered} f^{\prime}(x)=x^2-3x+12\text{ } \\ f(x)=\int (x^2-3x+12) \end{gathered}[/tex][tex]\int (x^2-3x+12)=\frac{x^3}{3}-\frac{3x^2}{2}+12x+c[/tex]To find c substitute x by 0 and y by 9 because f(0) = 9
[tex]\begin{gathered} f(x)=\frac{1}{3}x^3-\frac{3}{2}x^2+12x+c \\ f(0)=\frac{1}{3}(0)^3-\frac{3}{2}(0)^2+12(0)+c=9 \\ c=9 \end{gathered}[/tex]The function f(x) is
[tex]f(x)=\frac{1}{3}x^3-\frac{3}{2}x^2+12x+9[/tex]Answer D
Help in solving for y. Need to know the slope and y-intercept in the equation
Given the following equation:
8x - 5y = 10
then, we can solve it for y as follows:
5y = 8x -10
y = (8/5)x - (10/5)
y = (8/5)x - 2
So, the slope is m = 8/5 and the y-intercept is yo = -2.
4) Math Club members want to advertise their fundraiser each week in the school paper. They knowthat a front-page ad is more effective than an ad inside the paper. They have a $30 advertisingbudget. It cost $2 for each front-page ad and $1 for each inside page ad. The club wants to advertiseat least 20 times. a) Write and graph a system of inequalities to model the number of advertisements the club canpurchase to stay under budget. Be sure to label all parts of your graph.b) State one solution that would work. How much money will remain in the club's budget?
Problem:
Math Club members want to advertise their fundraiser each week in the school paper. They know that a front-page ad is more effective than an ad inside the paper. They have a $30 advertising budget. It cost $2 for each front-page ad and $1 for each inside page ad. The club wants to advertise at least 20 times.
a) Write and graph a system of inequalities to model the number of advertisements the club can purchase to stay under budget. Be sure to label all parts of your graph.
Solution:
Let us denote the number of front-page ads by x, and the number of inside ads by y:
x = number front-page ads
y= number of inside ads
Now, because they have a $30 advertising budget and It cost $2 for each front-page ad and $1 for each inside page ad, the first inequality that we have is:
[tex]2x+\text{ y }\leq30[/tex]If we represent the graph of the equality (line) 2x+y = 30, we have:
On the other hand, because the club wants to advertise at least 20 times, the second inequality that we have is:
[tex]x+y\ge20[/tex]If we represent the graph of the equality (line) x+y = 20, we have:
Now, the intersection point of the above lines, that is 2x+y = 30 and x+y = 20 is found as follows:
we have
y = 30 - 2x
and
y = 20-x
then
30-2x = 20-x
and
30-20 = 2x-x
that is
10 = x
when x = 10 then y = 20-x = 20-10 = 10
Kayla wants to have new doors installed in herhome. A door company charges a one-time fee of$125 plus $ per window installed. Write anexpression that represents the total cost to installnew windows in terms of the number of windows(w) installed.
Kayla wants to have new doors installed.
The door company charges $125 as a one time fee.
They also charge $50 per window installed.
If the number of new windows installed is w, then it means that to install w new windows, they will charge an additional:
w * 50 = $50w
This will be in addition to the one time fee.
Let T be the total cost of installation.
Therefore, the total cost for installing w new windows (in dollars) is:
T = 125 + 50w
8x +1312x + 7X == [?]Enter
The two angles given in the problem lie the opposite of each other with respect to the transversal line. This means that these two angles are supplementary angles. The sum of the two angles will be equal to 180 degrees, hence, we can set up an equation solving for x. We have
[tex]8x+13+12x+7=180[/tex]Solve for x, we have
[tex]\begin{gathered} 20x+20=180 \\ 20x=180-20 \\ \frac{20x}{20}=\frac{160}{20} \\ x=8 \end{gathered}[/tex]The value of x
A string that is 10 1/2 feet long is cut into 3 equal pieces. How long is each piece?
Answer:
3½
Step-by-step explanation:
10½=21/2
since it is cut into 3 pieces we can as well said it is divided into 3
21/2 divide 3
21/2 / 3/1
21/2 ×1/3
=7/2
=3½
please rate as brainliest
Answer:
The answer is 3.5
Step-by-step explanation:
Why?
Because since we know we have to divide the measurement of the string with the amount of pieces which will be
= 10 1/2 divided by 3
How long is each piece= 3.5
So that means each piece is 3.5
Hope this answers your question!
consider the polynomial function p given by p(x)=7x³-2x²+3x+10. Evaluate the function at x = -3.
Answer: -206
Step-by-step explanation:
[tex]p(-3)=7(-3)^3 -2(-3)^2 +3(-3)+10=-206[/tex]
Transforming the graph of a function by reflecting over an axis
ANSWER:
(a)
(b)
STEP-BY-STEP EXPLANATION:
(a)
We must do the following transformation:
[tex]y=f(x)\rightarrow y=f(-x)[/tex]In this case, reflects f(x) about the y-axis. The rule that follows the above, is like this:
[tex](x,y)\rightarrow(-x,y)[/tex]We apply the rule to the points of the function and it would be:
[tex]\begin{gathered} \mleft(-4.2\mright)\rightarrow(4,2) \\ (0,4)\rightarrow(0,4) \\ (4,6)\rightarrow(-4,6) \end{gathered}[/tex]We graph and we have:
(b)
We must do the following transformation:
[tex]y=g(x)\rightarrow y=-g(x)[/tex]In this case, reflects f(x) about the x-axis. The rule that follows the above, is like this:
[tex](x,y)\rightarrow(x,-y)[/tex]We apply the rule to the points of the function and it would be:
[tex]\begin{gathered} \mleft(-7,-2\mright)\rightarrow\mleft(-7,2\mright) \\ \mleft(-4,-5\mright?)\rightarrow\mleft(-4,5\mright) \\ \mleft(4,-1\mright)\rightarrow\mleft(4,1\mright) \end{gathered}[/tex]We graph and we have:
A certain Greenland shark is 37 cm long at birth and grows 0.75 cm / year. A certain spiny dogfish shark is 22 cm long at birth and grows 1.5 cm/year. When will the sharks be equal in length? Let x = time in years Let y = length of the sea creatures
In 20 years the length of shark will be equal.
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
A certain Greenland shark is 37 cm long at birth and grows 0.75 cm / year.
. A certain spiny dogfish shark is 22 cm long at birth and grows 1.5 cm/year.
Let x = time in years Let y = length of the sea creatures
So, the equation can be written as
For Green land shark: y= 37+ 0.75x
For Spiny Dogfish: y= 22 + 1.5x
When both equation are equal
37+ 0. 75x = 22 + 1.5x
37- 22 = 1.5x - 0.75x
15 = 0.75x
x= 15/0.75
x= 20
and, y= 22 + 1.5(20)= 52
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The heights, in feet, of 12 trees in a park are shown below.8, 11, 14, 16, 17, 21, 21, 24, 27, 31, 43, 47Use the drop-down menus to explain the interquartile range of the data.
Given:
The heights, in feet, of 12 trees in a park are:
8,11,14,16,17,21,21,24,27,31,43,47.
Required:
To find the interquartile range of the given data.
Explanation:
We have given the heights of 12 trees in feet.
Therefore, the total number of quantitties (elements) in given data is even.
Thus, the median (M) of the data is,
[tex]\begin{gathered} M=\frac{21+21}{2} \\ \Rightarrow M=\frac{42}{2} \\ \Rightarrow M=21 \end{gathered}[/tex]The median (Q) of the first half of the data 8,11,14,16,17 is given by,
[tex]Q=14[/tex]since the number of quantities are odd.
The median (Q') of the second half of the data 24,27,31,43,47 is given by,
[tex]Q^{\prime}=31[/tex]since the number of quantities are odd.
Hence, the interqurtile range (R) is,
[tex]\begin{gathered} R=Q^{\prime}-Q \\ \Rightarrow R=31-14 \\ \Rightarrow R=17 \end{gathered}[/tex]Final Answer:
The interquartile range is,
[tex]R=17[/tex]The first option is spread.
The second option is range.
The third option is 17.
The fourth option is middle 50%.
If the function rule is to add 6, and an output value is 6, what is the input value?options:01-612
Given,
If the function rule is to add 6, and an output value is 6.
To find: What is the input value?
Solution:
When we add 0 to any number, we got the same number.
So adding 0 with 6 we get the same number 6.
[tex]6+0=6[/tex]Thus, the answer 0 is the correct option.
Which of the following is equivalent to - sin ¹1?A. sin ¹111OB. - sin(-11)OC. sin(-11)D. sinReset Selection
The correct option is C.
If an investment grew to $13,500 in 2 years and the interest amount earned was $1,150, calculate the nominal interest rate compounded quarterly.
The nominal interest rate compounded quarterly is 1.33%.
Given,
If an investment grew to $13,500 in 2 years.
and, the interest amount earned was $1,150.
To find the nominal interest rate compounded quarterly.
What is nominal interest rate?
The interest rate before inflation is referred to as the nominal interest rate.
Nominal can also refer to the advertised or stated interest rate on a loan, excluding any fees or interest compounding.
Now, According to the question:
Here given ,
P = $13500
i = ?
A = $1150
t = 2 yrs
n = 4 x 2 = 8
Formula of compound interest ,
A = P( 1 + I )ⁿ
$1150 = $13500 ( 1 + i ) ⁸
$1150 / $13500 = (1 + i)⁸
0.0851 = (1+ i) ⁸
1 +i = 8√.0851
1 + i = 2.33
i = 2.33 -1
i = 1.33 %
Hence, The nominal interest rate compounded quarterly is 1.33%.
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If the scale factor is 4, what is the measurement of x?24 m4 m20 m16 m
Let:
[tex]\begin{gathered} 6k=x \\ \end{gathered}[/tex]where:
k = scale factor
If the scale factor is 4, then:
[tex]\begin{gathered} 6(4)=x \\ 24=x \\ x=24 \end{gathered}[/tex]A. Find the zeros in state the multiplicity of each zeroB. Write an equation expressed as the product of factors, of a polynomial function for the graph Using A leading coefficient of 1 or -1 and make the degree of F a small as possible.C. Use both the equation in part B and graph to find the Y intercept
Given the graph of a polynomial function:
We will find the following:
A. Find the zeros and state the multiplicity of each zero
The zeros of the function are the points of the intercept between the x-axis and the graph of the function
as shown, there are 3 points of intersection (3 zeros)
x = -1, multiplicity = 3
x = 1, multiplicity = 2
x = 2, multiplicity = 1
B. Write an equation expressed as the product of factors, of a polynomial function for the graph Using A leading coefficient of 1 or -1 and make the degree of F as small as possible.
Form A, the factors of the function will be:
(x+1), (x-1), and (x-2)
The equation of the function will be:
[tex]f(x)=(x+1)^3(x-1)^2(x-2)[/tex]C. Use both the equation in part B and graph to find the Y-intercept
The y-intercept is the value of (y) when (x = 0)
So, substitute with x = 0
So,
[tex]y=(0+1)^3\cdot(0-1)^2\cdot(0-2)=-2[/tex]So, the answer will be: y-intercept = -2
writing to explain in your own words tell what it meant by the absolute value of an integer
An absolute value of an integer is defined as a positive value/ digit of an integer regardless of the sign.
The symbol used is as shown below;
[tex]\parallel\text{ -3 }\parallel[/tex]or single lines as;
This means in absolute value of an integer , negative 2 is equal to positive 2.
Answer
In summary, an absolute value of an integer is a non-negative value , and the sign will only indicate direction, if well stated.
find the explict formula for 15, 12, 9, 6
Given:
15, 12, 9, 6
To write the explicit formula, use the form:
[tex]a_n=a_1+d(n-1)[/tex]Where
a1 = first term = 15
d = common difference = 12 - 15 = -3
n = number of terms
Therefore, the explicit formula is:
[tex]\begin{gathered} a_n=15-3(n-1) \\ \\ a_n=15-3n+3 \\ \\ a_n=18-3n \end{gathered}[/tex]ANSWER:
[tex]a_n=18-3n[/tex]Meg owes the bank more than $15. Use , or = to make the statement true. Meg's account value ? -$15 2 What is the value of point A? ? How far is point A from 0 (absolute value)? || HAR
Answer; Meg's account is < - $15
Meg is owing the bank more than -$15
This implies that, the amount she is owing is more that -$15
The amount she is owing the bank could be -$16, -$17
Therefore, her current back account is less than -$15
Meg's account value is < -$15
JCPenney sells jeans for $49.50 that cost $38.00. What is the percent markup on cost? Check the cost.
The percent markup of the jeans is 30.2%
How to calculate the markup on cost ?
The selling price of the jeans is $49.50
The cost price is $38
Markup can be described as the difference between the selling price and the cost price of a product
The markup can be calculated by subtracting the cost price from the selling price
= 49.50 - 38
= 11.5
The percent markup can be calculated as follows
11.5/38 × 100
= 0.302 × 100
= 30.2%
Hence the percent markup is 30.2%
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what is the answer help pls
Answer:
1 ½ feet
Step-by-step explanation:
The shortest lizard is ½ a feet
The longest lizard is 2 feet
To find the difference in length:
2-½ = 1½ feet