The quadratic equation is y = 4. (x + 2)(x - 1).
Given,
The roots are -2 and 1 and whose leading coefficient is 4 using the letter x to represent the variable.
To Write the Quadratic Equation by using above given:
Now, According to the question:
Roots are -2 and 1
Leading Coefficient is = 4
Using Variable is = x
Formulate the equation of polynomial function is
y = 4. (x + 2)(x - 1)
Hence, The quadratic equation is y = 4. (x + 2)(x - 1).
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Sam starts travelling at 4 km/h from a campsite 2 hours ahead of Sue, who travels 6 km/h in the same direction. How many hours will it take for Sue to catch up to Sam?
Sue take 4 hours to catch up Sam. The question is about speed, distance and time
So for this, the formula is given
speed (s) = distance(d) / time(t)
According to question,
Speed of Sam is = 4 km/h
Distance covered by Sam = 4 * 2
= 8 km
Speed of Sue = 6 km/hr
Now, Sam and Sue are in same direction so minus the speed
speed = 6 - 4
= 2 km/hr
Now, we have speed = 2km/hr and
distance = 8km find the time,
put the values in formula, s = d/t
2 = 8/t
t = 8/2
t = 4 hours
Therefore, Sue take 4 hours to catch up Sam.
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Triangle END is translated using the rule (x, y) → (x−4, y − 1) to create triangle E′N′D′. If a line segment is drawn from point E to point E′ and from point N to point N′, which statement would best describe the line segments drawn?
Given:
Triangle END is translated using the rule
[tex](x,y)\rightarrow(x-4,y-1)[/tex]to create triangle E′N′D′.
Required:
We need to describe the line segment when a line segment is drawn from point E to point E′ and from point N to point N′,
Explanation:
Let E(0,0), N(2,0), and D(0,2) be the points of the triangle END.
Use the translation rule to find the triangle E'N'D'.
Substitute x =0 and y =0 in the translation rule.
[tex]E(0,0)\rightarrow E^{\prime}(0-4,0-1)[/tex][tex]E(0,0)\rightarrow E^{\prime}(-4,-1)[/tex]Substitute x =2 and y =0 in the translation rule.
[tex]N(2,0)\rightarrow N^{\prime}(2-4,0-1)[/tex][tex]N(2,0)\rightarrow N^{\prime}(-2,-1)[/tex]Substitute x =0 and y =2 in the translation rule.
[tex]D(0,2)\rightarrow D^{\prime}(0-4,2-1)[/tex][tex]D(0,2)\rightarrow D^{\prime}(-4,1)[/tex]We get the point E'(-4,-1), N'(-2,-1), and D'(-4,1).
Mark the points E(0,0), N(2,0), D(0,2), E'(-4,-1), N'(-2,-1), and D'(-4,1) on the graph and draw a line segment from point E to point E′ and from point N to point N′,
From the figure, we get that the lines are parallel and congruent.
Final answer:
They are parallel and congruent.
Lisa and Susan are driving to college together. They look at a map to find out how far they have to drive. On the map, Lisa measures the distance to be 4.5 inches. How many miles do they have to drive if the map scale is 1 in. = 35 mi?
Answer:157.5
Step-by-step explanation:becuase mutilpy 4.5x35 that equals 157.5
Please help! Create a scatterplot for the data in the table. Let English scores be X and History Scores be Y.
Part 2: draw line of fit
Part 3: choose two points, find slope, and record slope decimal
For the given question.
x-axis contains the independent variables "English score."
y-axis contains the dependent variables "History score."
The graph for the given table is plotted with the scattered points.
Let us take two points from the graph,
(x₁,y₁) = (60, 65)
(x₂, y₂) = (61, 61)
Then the slope will be;
slope = m = (y₂ - y₁)/(x₂ - x₁)
Put the values.
m = (61 - 65)/(61 - 60)
m = -4
Thus, the slope of the line is found as -4.
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As shown in the diagram below, ABC || EFG andBF EF.
Now:
[tex]\begin{gathered} BF\cong EF \\ \angle BEF=\angle EFB=42.5 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \angle EBF=180-\angle BEF-\angle EFB \\ \angle EBF=180-42.5-42.5 \\ \angle EBF=180-85 \\ \angle EFB=95 \end{gathered}[/tex]Question in picture will give brainlist
The correct options are first : ∠3 + ∠4 = 180°, third : ∠1 and ∠2 are a linear pair, fourth : ∠2 = ∠4, and fifth : ∠1 = ∠3.
We are given a diagram that has two straight lines that intersect at a point.This results in the formation of four angles ∠1, ∠2, ∠3, and ∠4.The first option is ∠3 + ∠4 = 180°.It is true because ∠3 and ∠4 form a linear pair and are on the same side of the line.The second option is ∠1 = ∠2.It is false because we don't see any relationship between the two angles as such.The third option is ∠1 and ∠2 are a linear pair.It is true because ∠1 + ∠2 = 180°.The fourth option is ∠2 = ∠4.It is true because they are vertically opposite angles.The fifth option is ∠1 = ∠3.It is true because they are vertically opposite angles.To learn more about angles, visit :
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Sharpe Razor Company has total assets of $1,870,000 and current assets of $667,000. It turns over its capital assets one times a year and has $335,000 of total debt. Its return on sales is 5 percent. What is Sharpe’s return on shareholders' equity?
If Its return on sales is 5 percent. Sharpe’s return on shareholders' equity is 8.26%.
How to find the return on shareholders' equity?First step is to find the fixed asset
Fixed asset = $1,870,000 + $667,000
Fixed asset = $2,537,000
Second step is to find the sales
Sales = Total assets × Fixed asset turnover
Sales = $2,537,000 × 1
Sales = $2,537,000
Third step is to find the stockholder equity
Stockholder equity = $1,870,000 - $335,000
Stockholder equity = $1,535,000
Fourth step is to find the net income
Net income = $2,537,000 × 5%
Net income = $126,850
Now let find the return on shareholders' equity
Return on shareholders' equity = Net income / Shareholders' equity
Return on shareholders' equity = $126,850 /$1,535,000
Return on shareholders' equity = 8.26%
Therefore 8.26% is the return on shareholders' equity.
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The tank of a car holds 10 gallons of gas. How many liters does the tank hold?
Given:
The tank of a car holds 10 gallons of gas.
To find the number of liters does the tank hold:
As we know,
1 gallon = 3.785 liters
So that, for 10 gallons
[tex]\begin{gathered} =10\times3.785 \\ =37.85\text{ liters} \end{gathered}[/tex]Thus, the tank can hold 37.85 liters of gas.
Bryan Joan had 261 dollars to spend on 8 books. After buying them he had 13 dollars. How much did each book cost?
Answer:
8
Step-by-step explanation:
.
Find the length of the sides of a triangle with vertices at (0,-4), (-2,5) and (10,7).
The side lengths of the triangle with vertices at (0,-4), (-2,5) and (10,7). are √85, √148 and √221
How to calculate the side lengths of the triangle?From the question, we have
The triangle with vertices at (0,-4), (-2,5) and (10,7).
The side lengths of the triangle is then calculated using the following distance formula
d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
Where x and y are the coordinates of the triangle
For vertices at (0,-4) and (-2,5), we have
d = √[(0 + 2)²+ (-4 - 5)²]
Evaluate
d = √85
For vertices at (-2,5) and (10,7). we have
d = √[(-2 - 10)²+ (5 - 7)²]
Evaluate
d = √148
For vertices at (0, -4) and (10,7). we have
d = √[(0 - 10)²+ (-4 - 7)²]
Evaluate
d = √221
Hence, the side lengths are √85, √148 and √221
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The entire graph of the function f is shown in the figure below.
Write the domain and range of f as intervals or unions of intervals.
The domain of the function f is [-5. -2] U [ 1, 2].
The range of the function f is [-4, 3].
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
A graph of the function f.
We can see two curves on the graph.
One curve:
Domain = [1, 2]
Range = [-4, 0]
Other curve:
Domain = [-5, -2]
Range = [-3, 3]
We can combine both the curve domain and the range.
Domain = [-5. -2] U [ 1, 2 ]
Range = [-4, 3]
Thus,
The domain of the function f is [-5. -2] U [ 1, 2].
The range of the function f is [-4, 3].
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What is the slope of the line described by the equation y+3=-2x
Using the equation of the line, the slope of the line is -2.
How to find the slope of a line?The slope of a line is the change in y with respect to the change in x.
In other words, slope is rise over run.
Therefore, the equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptHence, we will rearrange the equation of the line to get the slope of the line.
y + 3 = - 2x
y = -2x - 3
Therefore, the slope is -2.
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y = 3x - 4
m=?
b= ?
Answer:
m = 3 , b = - 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx b ( m is the slope and b the y- intercept )
y = 3x - 4 ← is in slope- intercept form
with m = 3 and b = - 4
Here is the probability model for the blood type of a randomly chosen person in the United States.Blood typeoАBABProbability 0.42 0.21 0.07 0.3What is the probability that a randomly chosen American does not have type o blood?% Round to the nearest 0.01%
The total probability = 0.4 + 0.21 + 0.07 + 0.3 = 1
Given that the probability that a randomly chosen American has a type O blood is 0.42, then, the probabillity that a randomly chosen American does not have a type O blood is
1 - 0.42 = 0.58
= 58 x 100 = 58%
32 divided by 27,215 
Answer: 850 R 4
Step-by-step explanation:
Answer:
Is is 0.00117582215
Step-by-step explanation:
I hooked it up
Find the union of A and B.Select the correct answer below:{2.5,b,4,f,1/2,c,4.1,a,3,1/3}{2.5,4,1/2,4.1,3,1/3}{b,f,c,a}{2.5,b,1/2,c,4.1,a,3,1/3}
EXPLANATION:
Given;
We are given two sets A and B with the elements as indicated in the attached image.
Required;
We are required to find the union of sets A and B.
Solution;
The union of two sets is given as the elements contained in set A, in set B and the intersection of both.
The elements of set A are;
[tex]A=\lbrace2.5,b,4,f,\frac{1}{2},4.1,c\rbrace[/tex]The elements of set B are;
[tex]B=\lbrace a,3,\frac{1}{3},\frac{1}{2},4.1,c\rbrace[/tex]The intersection of both sets are:
[tex]A\cap B=\lbrace\frac{1}{2},4.1,c\rbrace[/tex]Taking all elements common to both sets A and B including the intersection, we now have the union of both sets;
ANSWER:
[tex]A\cup B=\lbrace2.5,b,4,f,\frac{1}{2},c,4.1,a,3,\frac{1}{3}\rbrace[/tex]The first option is the correct answer.
in the figure above what is the value of X what is the measure is side WZ
Based on the diagram, we have two right triangles. These are triangle WYT and triangle WYZ.
Since both legs of each triangle is congruent to each other, we can also say that their hypotenuse are congruent too.
Thus, TW = WZ or 2x = 3x - 5.
From this, we can now solve for x.
[tex]\begin{gathered} 2x=3x-5 \\ \text{Subtract 3x on both sides.} \\ 2x-3x=3x-3x-5 \\ -x=-5 \\ \text{Divide by -1 on both sides.} \\ x=5 \end{gathered}[/tex]Therefore, the value of x = 5.
To solve for WZ, let's plug in x = 5 to 3x - 5.
[tex]\begin{gathered} WZ=3x-5 \\ WZ=3(5)-5 \\ WZ=15-5 \\ WZ=10 \end{gathered}[/tex]Therefore, WZ = 10.
To summarize, x = 5 and WZ = 10. (Option A)
HELP ASAP
Easy math, for old review notes.
Consider the expression:
8f – 5g + 6h – 10j + 2
How many terms does the expression have?
What is the constant of the expression?
What is the fourth term in the expression?
What is the coefficient of the third term?
In the given expression, the number of terms is 5, the constants are 8, -5 6, -10 and 2. The fourth term is j and the coefficient of the third term is 6
What are Mathematical ExpressionsIn mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An algebraic expression consists of unknown variables, numbers and arithmetic operators. It does not contain any equality or inequality symbols. An expression in math is a statement involving at least two different numbers (known or unknown) and at least one operation.
In the given expression, we have to answer some questions here;
a) The number of terms in the expression is 5
b) The constant of the expression are 8, -5, 6, -10 and 2
c) The fourth term in the expression is j
d) The coefficient of the third term is 6
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the student council raised 2,790 during its annual fundraiser. the money was shared equally among the events committee the sports committee and the sunshine committee. the sports committee wants to use its share of the money to purchase t shirts. if each t shirt costs $12 what is the greatest number of t shirts the sport committee purchase
The student council raised $2,790 and they have to shared equally among 3 comittees, then:
[tex]\frac{2,790}{3}=930[/tex]Each commitee has a budget of $930, then for the sports committee that wants to purchase t-shirts and each t-shirt costs $12, we can create the following expression:
Let x be the greatest number of t-shirts
[tex]\begin{gathered} 12x=930 \\ x=\frac{930}{12} \\ x=77.5 \end{gathered}[/tex]Rounding, the sport commitee can purchase 77 t-shirts.
HELP ASAP PLS PLS PLS
Jimmy earned $6840 from the gift basket sold
What is selling price ?
The selling price is how much a buyer pays for a product or service.
Given,
Number per basket for fruits = 12
Total number of fruits shipped last year = 3,420
Per basket price = $24
Now, we have to find total number of baskets
Total number of baskets = 3420 / 12
= 285
Total amount jimmy earned = 285 * 24
= $6840
Therefore, Jimmy earned $6840 from the gift basket sold.
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So there's a question and it's like a parallelogram and it's for question true and it's 10' by 5' and I'm trying to find out that area
we have that
the area of a parallelogram is
A=b*h
we have
b=10 ft
h=5 ft
so
A=10*5=50 ft2
area is 50 square feetfind the area of the shaded sector in terms of Pi
Danny has $2.14 worth of pennies and nickels in his piggy bank. The number of nickels is two more than ten times the number
of pennies. How many nickels and how many pennies does Danny have?
Danny has 42 nickels and 4 pennies.
The total amount of Danny in the piggy bank is $2.14.The money in Danny's bank consists of pennies and nickels.We know that a penny is worth $0.01.We also know that a nickel is worth $0.05.We are given the fact that the number of nickels is two more than ten times the number of pennies.Let the number of pennies be denoted by "x".Then the number of nickels is "10x + 2".The total amount of money because of just the pennies is $0.01*x.The total money because of just the nickels is $0.05*(10x + 2).We know that the total amount is $2.14.We can form an equation with the available data.0.01*x + 0.05*(10x + 2) = 2.140.01x + 0.5x + 0.1 = 2.140.51x = 2.04x = 4The number of pennies is 4.The number of nickels is 42.To learn more about equations, visit :
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Let f(x) = 9x-2 and g(x)=√√3x +7. Evaluate the following. a g (3)-g (-2) b (g (-1))² Let f(x) -f(0)/x
The given functions are f(x) = 9x-2 and g(x)=√(√3x +7) the value of f (3) and g (3) will be 25 and 3.4592.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that f(x) = 9x-2 and g(x)=√√3x +7.
We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.
We have to evaluate the values one by one putting the value of an independent variable as,
a) g (3)
g(x)=√(√3x +7)
g(3) = √(√3(3) +7)
g(3) =√(5.196 + 7 )
g(3) =√(12.196)
g(3) =3.492
b)f (3)
f(x) = 9x-2
f(3) = 9× 3 -2
f(3) = 27 - 2
f(3) = 25
Thus, the given functions are f(x) = 9x-2 and g(x)=√(√3x +7) the value of f (3) and g (3) will be 25 and 3.4592.
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Order the expressions by choosing <, >, or =.
The expression is
[tex]6^{-2}[/tex] < [tex]\frac{1}{6} ^{-2}[/tex] , [tex]6^{-1}[/tex]< [tex]\frac{1}{6} ^{-1}[/tex], [tex]6^{-2}[/tex]< [tex]6^{-1}[/tex]
Here we have to find the expression
a) [tex]6^{-2}[/tex] and [tex]\frac{1}{6}^{-2} }[/tex]
= 1/6² and 6²
= 1/ 36 and 36
= 1/36 < 36
So [tex]6^{-2}[/tex]< [tex]\frac{1}{6} ^{-2}[/tex]
b) [tex]6^{-1}[/tex] and [tex]\frac{1}{6} ^{-1}[/tex]
= 1/6 and 6
= 1/6 < 6
So [tex]6^{-1}[/tex] < [tex]\frac{1}{6} ^{-1}[/tex]
c) [tex]6^{-2}[/tex] and [tex]6^{-1}[/tex]
= 1/36 and 1/6
= 1/36 < 1/6
So [tex]6^{-2}[/tex] < [tex]6^{-1}[/tex]
Therefore the expression is [tex]6^{-2}[/tex]< [tex]\frac{1}{6} ^{-2}[/tex] , [tex]6^{-1}[/tex] < [tex]\frac{1}{6} ^{-1}[/tex] , [tex]6^{-2}[/tex] < [tex]6^{-1}[/tex].
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yaretzyΣ 21. $1,500 is deposited into a savings account that earns 2.5% simple interest for 4years. How much interest will be earned in the 4 years? *Your answer
We have the next formula to the simple interest
[tex]I=P\times r\times t[/tex]where
I= interest earn after t years
P is the initial deposit
r is the rate
t is the time
P=1500
r=2.5%
t= 4 years
then we substitute the values in the formula
[tex]I=1500(.025)(4)[/tex][tex]I=150[/tex]He will earn $150 after 4 years, his final capital will be $1650
Given f(x), use Remainder Theorem to find f(4). f (x) = 2x^3 – 11x^2 + 7x - 5
To find f(4) you divide the given polynomial into (x-4):
To divide:
1. Divide the first term of the dividend by the highest term of the divisor:
[tex]\frac{2x^3}{x}=2x^2[/tex]2. Multiply the divisor by the result:
[tex]2x^2(x-4)=2x^3-8x^2[/tex]3. Substract the product in step 2 from the appropiat terms of the dividend (when you substract the symbols change) (then bring down the next term from the dividend)
4. Repeat previous steps:
[tex]\frac{-3x^2}{x}=-3x[/tex][tex]-3x(x-4)=-3x^2+12x[/tex][tex]\frac{-5x}{x}=-5[/tex][tex]-5(x-4)=-5x+20[/tex]As the remainder is -25:
[tex]f(4)=-25[/tex]Hi, my son just started virtual learning and school not providing much help so far. Need help with step by step (show work) with these 4 problems to double check homework…x= (guess I can only ask one per time?! New to this…
Solution
Step 1
Use the secant and tangent theorem to a circle.
Step 2
AC = 30 + x
BC = x
CD = 20
Step 3
Substitute into the theorem
[tex]\begin{gathered} (30+x)\times x\text{ = 20}^2 \\ \\ x^2+30x\text{ = 400} \\ \\ x^2+30x-400=0 \end{gathered}[/tex]Step 4
Use the factorization method to solve for x.
[tex]\begin{gathered} x^2+30x-400=0 \\ \\ x^2-10x+40x-400=0 \\ \\ x(x-10)+40(x-10)=0 \\ \\ (x+40)(x-10)=0 \\ \\ x-10=0,\text{ x+40=0} \\ \\ x\text{ = 10, x = -40} \end{gathered}[/tex]Step 5
The value of x cannot be negative, hence x = 10
Final answer
x = 10
consider triangles MNP and TUV which statement must be true?answer questions and the question to the problem is in the image
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
From the question, we can see that triangle MNP has three angles
which are:
[tex]\begin{gathered} 88^{0\text{ }},61^{0\text{ }}and^{} \\ 31^0 \end{gathered}[/tex]while Triangle TUV has three angles which are:
[tex]\begin{gathered} 79^0,40^{0\text{ }}and^{} \\ 61^0 \end{gathered}[/tex]Hence, it is easy to see that the correct option is:
[tex]\Delta\text{ MNP is not similar to }\Delta\text{ TUV ( OPTION A)}[/tex]
6#Suppose that IQ scores in one region are normally distributed with a standard deviation of 17. Suppose also that exactly 58% of the individuals from this region have IQ scores of greater than 100 (and that 42% do not). What is the mean IQ score for this region? Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.
ANSWER:
103.4
STEP-BY-STEP EXPLANATION:
Given:
Standard deviation (σ) = 17
x = 100
The probability is 42%, that is 0.42, we look for this value in the normal table to determine the value of z as follows:
z = -0.2
Knowing that value we can calculate the mean, just like this:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ \text{ We replacing:} \\ \\ -0.2=\frac{100-\mu}{17} \\ \\ 100-\mu=-0.2\cdot17 \\ \\ \mu=100+0.2\cdot17 \\ \\ μ=103.4 \end{gathered}[/tex]The mean is equal to 103.4
