The quadratic equation whose roots are -6 and 3/4 is 14x²+21x-18=0
How to find quadratic equations?We should know that a quadratic equation is that whose highest power of the variable is 2
The given roots are
x=-6 and x=3/4
Let (x+6)(x-3/4)=0
Multiplying the brackets we have
[tex]X^{2}-\frac{3x}{4} +6x-\frac{18}{4}[/tex] =0
Find the LCM of the denominators
[tex]\frac{4X^{2}+21x-18 }{4} =0[/tex]
Cross and multiplying we have
[tex]4x^{2} +21x-18=0[/tex]
Therefore, the equation is expressed in the form ax²+bx+v=0 Where a=4, b=21 and c=-18
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I need the answer fast
a. Economic theory describes the relationship between inflation and unemployment as:
O positive.
O negative.
O independent
b. Using real-world data, this theory:
O is never found to be true.
holds only for certain time periods.
holds for all time periods.
c. True or false: Economists unanimously agree with the Phillips curve representation of unemployment and inflation in the
real world.
False
True
Answer:
1: The correction option is B) Negative
Explanation
In economic theory, the Philips curve depicts the relationship between unemployment and inflation as a negative one. In order words, when inflation goes up, unemployment reduces.
The logic behind that thinking is, that inflation, which is the general increase in prices of goods/commodities and services is good for business. Business owners are quick to adjust to higher prices regardless of how it is induced and sometimes even profit from it in sectors not affected by inflation. So in such sectors, as business improves, it is assumed that there is a requirement to being in more hands to help with the expansion of the business.
2. The correct option is B) Holds for certain time periods
Explanation
Social scientists and researchers have plotted the data across various periods (20 years) using data from the US economy.
The following results emerged:
the traditional relationship between inflation and unemployment held in 2001 during the mild recession triggered by the 9/11 situation. Unemployment took an upward spiral averaging an increase of 6% while inflation nosedived by 2.5%;Another snapshot was taken in the mid-2000s. This time unemployment went belly-up by several degrees, while inflation took off in the opposite direction by almost 5% before receding in 2006 when unemployment bottomed; In another analysis, the consumer price index took a steep downward dive during the Great Recession. This time, unemployment took a bullish charge, going up as much as 10%This negative relationship failed to hold between 2012 to 2015. Both factors developed a positive relationship and moved in the same direction; There has also been a loss of strength in the negative relationship as also seen in recent times. Specifically, between 2016 to 2019 where unemployment has steadily receded to 50-year lows, with inflation remained steady at an average of 2%.So the correct answer is B.
3. The correct answer is True:
Explanation
As seen from the analysis above, the negative relationship remains largely true for most of the periods examined. Hence it is more pragmatic to expect a dip in unemployment whenever there is a spike in the CPI.
Cheers
**Help Needed**
The picture below is a sketch of a picnic area with a courtyard. How much of the courtyard is available for use?
Answer:
87 m²
Step-by-step explanation:
The picnic area is the white inner rectangle, while the courtyard is the outer pink rectangle.
The area of the courtyard available for use = area of the pink rectangle - area of the white rectangle
✔️Area of the courtyard (pink rectangle) = L*W
L = 13 m
W = 7 m
Area of pink rectangle = 13*7 = 91 m²
✔️Area of the picnic (white rectangle) = L*W
L = 4 m
W = 1 m
Area = 4*1 = 4 m²
✅Area available in the courtyard for use = 91 m² - 4 m² = 87 m²
Solve for x and show work!
Answer: x=8
Step-by-step explanation:
We know that it is a square, so the diagonals divide the four triangles evenly.
A whole circle will have 360°. When it is divides into 4, each angle will be
360/4=90°
The vertex of each triangle will be 90°
And the given vertex equation is 8x+26
8x+26=90
8x+26-26=90-26
8x=64
x=8
Hope this helps!! :)
Please let me know if you have any questions
Type the correct answer in each box. Use numerals instead of words.
Consider function h.
What are the values of the function when x= 0 and when x=4
h(0)=
h(4)=
Answer:
10 16
Step-by-step explanation:
when x= 0 h(x)=2x²-3x+10
⇒ h(0)=2*0²-3*0+10=10
when x= 4 h(x)=[tex]2^{x}[/tex]
⇒ h(4)=[tex]2^{4}[/tex]=16
The value of the given piecewise function at [tex]x=0[/tex] is [tex]h(0)=10[/tex] and the value of the function at [tex]x=4[/tex] is [tex]h(4)=16[/tex].
Important information:
The given piecewise function is:[tex]h(x)=\begin{cases}3x-4, &x < 0 \\ 2x^2-3x+10, &0\leq x < 4 \\ 2^x, & x\geq 4\end{cases}[/tex]
Piecewise Function:The function for [tex]x=0[/tex] is [tex]h(x)=2x^2-3x+10[/tex].
[tex]h(0)=2(0)^2-3(0)+10[/tex]
[tex]h(0)=10[/tex]
The function for [tex]x=4[/tex] is [tex]h(x)=2^x[/tex].
[tex]h(4)=2^4[/tex]
[tex]h(4)=16[/tex]
Therefore, the required values of the piecewise function are [tex]h(0)=10[/tex] and [tex]h(4)=16[/tex].
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A girl with a height of 5 ft casts a shadow of 2 ft. What would be the height of a building that casts a shadow 50 ft long at the same time?
Answer:The person is 5feet, 6inches Note: 12 inches= 1 foot, so 6 inches= 1/2 a feet and 6 inches= .5 feet
Step-by-step explanation:
Find the measures of the numbered angles in each kite. I need the answer as fast as possible!!!!!!
Answer:
1 = 20°
2 = 90°
3 = 70°
4 = 55°
An element with a mass of 700 grams decays by 6.1% per minute. To
the nearest tenth of a minute, how long will it be until there are 220
grams of the element remaining?
Answer
m =18.4 minutes
Step-by-step explanation:
220 = 700 x (0.939)^m
220/700 = (0.939)^m
m = Log(220/700) / Log(0.939)
m =18.4 minutes
Answer: the answer would be 18.4 minutes
Step-by-step explanation:
Cory is saving for his son's college education. If the savings account earns 2.8% interest
compounded monthly, and he wants to have $25,000 in 18 years, what must the principal
be? Round your answer to the nearest dollar.
Answer:
principal is $15112
Step-by-step explanation:
25000=P(1+ 0.028/12)^(12times18)
The principal amount of the savings is $15111.6
How to determine the principal amount?The given parameters are:
Interest rate, r = 2.8%Amount, A = $25,000Time, t = 18 yearsNumber of times compounded, n = 12 i.e. monthlyAmount is calculated using:
A = P(1 + r/n)^nt
So, we have:
25000 = P(1 + 2.8%/12)^(12 * 18)
Make P the subject
P = 25000/(1 + 2.8%/12)^(12 * 18)
Evaluate the expression
P = 15111.6
Hence, the principal amount is $15111.6
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Which equation is true for x = –6 and x = 2?
2x2 – 16x + 12 = 0
2x2 + 8x – 24 = 0
3x2 – 4x – 12 = 0
3x2 + 12x + 36 = 0
Answer:
x2 + 4x - 12
Step-by-step explanation:
(x + 6) ( x-2)
x2 - 2x + 6x - 12
x2 + 4x -12
Which unique sequence of rigid motions maps quadrilateral ABCD to quadrilateral EFGH?
6
5
A
IB
x
634
1 2 3 4 5 6
E
G
A
A reflection over the x-axis followed by a translation of (z,y) → (2, y - 4).
B. A reflection over the y-axis followed by a translation of (1,y) → (I, y-6).
C. A translation of (I, y) + (1, y-3) followed by a reflection over the y-axis.
A translation of (€,y) → (3-6, y) followed by a reflection over the x-axis.
Answer:
The unique sequence of rigid motions that maps quadrilateral ABCD to EFGH are;
B. A reflection over the y-axis followed by a translation of (I, y) → (I, y - 6)
('I' is the image of 'x' after reflection)
Step-by-step explanation:
The coordinates of the vertices of the quadrilateral ABCD are;
A(-5, 4), B(-2, 4), C(-2, 1), and D(-5, 2)
The coordinates of the vertices of the quadrilateral EFGH are;
E(5, -2), F(2, -2), G(2, -5), and H(5, -4)
By analysis, we have;
The signs of the x-coordinate of the preimage and the image are opposite, therefore, one of the rigid motions is a reflection across the y-axis
Similarly, the common difference between the y-coordinate values of the image and the preimage are;
-2 - 4 = -6
-2 - 4 = -6
-5 - 1 = -6
-4 - 2 = -6
The common difference between the y-coordinates of the image and the preimage is -6, therefore, the y-values are obtained by a translation of y - 6 units
Therefore, the unique sequence of rigid motions that maps quadrilateral ABCD to EFGH are a reflection over the y-axis followed by a translation of (I, y) → (I, y - 6).
wedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is to be held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population of about 2,000,000. 18) Suppose the wedding planner assumes that 5% of the guests will be pollotarian so she orders 15 pollotarian meals. What is the approximate probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals
Answer:
0.0793 = 7.93% probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
3.5% of the people in the area where a large wedding is to be held are pollotarian.
This means that [tex]p = 0.035[/tex]
300 guests
This means that [tex]n = 300[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.035[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.035*0.965}{300}} = 0.0106[/tex]
What is the approximate probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals?
This is 1 subtracted by the pvalue of Z when X = 0.05. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.05 - 0.035}{0.0106}[/tex]
[tex]Z = 1.41[/tex]
[tex]Z = 1.41[/tex] has a pvalue of 0.9207
1 - 0.9207 = 0.0793
0.0793 = 7.93% probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals
Answer:7.93%
Step-by-step explanation:
What is the value of x?
Enter your answer in the box.
Answer:
We say that a function is increasing on an interval if the function values increase as the input values increase ...
Step-by-step explanation:
Payne saves $2,000 at a yearly simple interest rate of 2%. He earns $280 in interest. How many years did he save his money?
Simplify 3x + 3 + 2
3x+5
5x+3
8×
Answer:
3x+5
Step-by-step explanation:
the cooler at a softball game holds 5 quarts of sports drink. how many cups of sports drink does the cooler hold
Answer: 20 cups :DD
Step-by-step explanation:
A part of an exponential function is graphed on the grid.
10
6
3
1
1
Which inequality best represents the domain of the part shown?
AX22
By 24.5
CX> 4.5
DY22
Answer:
x ≥ -2
Step-by-step explanation:
my teacher went over this with us
Simplify the expression by combining like terms:
5c2 + 13c + 4 – 7c + 9
Answer:
5c^2 +6c +13
Step-by-step explanation:
so we can see than 5c^2
and 13c - 7c are the same = 6c
and 4 +9 = 13
so answer will 5c^2 +6c +13
Answer:
[tex] {5c}^{2} + 6c + 13[/tex]
Step-by-step explanation:
1) Collect like terms.
[tex] {5c}^{2} (13c - 7c) + (4 + 9)[/tex]
2) Simplify.
[tex] {5c}^{2} + 6c + 13[/tex]
Therefor, the answer is 5c² + 6c + 13.
Complete the equation of the line whose y-intercept is (0, -1) and slope is 4.
(Khan academy)
Answer:
y = 4x - 1
Step-by-step explanation:
y = mx + b
Here m is slope and b is y-intercept
m = 4; b = -1
y = 4x - 1
I need this for math thanks
I’ll answer, but wait, do I send a picture of my work? or not? It says I have to make a table of values, so
Juanita is a 28-year old female college graduate from the South. Molly is a 28-year female college graduate from the West. Jennifer is a 28-year female college graduate from the Midwest. (i) Construct a 95% confidence interval for the difference in expected earnings between Juanita and Molly. (ii) Explain how you would construct a 95% confidence interval for the difference in expected earnings between Juanita and Jennifer.
Answer:
Hello your question has some missing information attached below is the missing information
answer :
i) ( 0.158 , - 1.018 )
ii) the difference in expected earnings can be computed as
( [tex]X_{6,A} - X_{5,C} ) = \beta _{0} + \beta _{6} - ( \beta _{0} - \beta _{5} ) = \beta _{6} - \beta _{5}[/tex]
Step-by-step explanation:
i) Construct a 95% confidence interval ( between Juanita and Molly )
Expected difference in earnings = ( X[tex]_{6}[/tex][tex]_{,A}[/tex] - X[tex]_{6.B}[/tex]) = [tex]\beta _{0}[/tex]= ( [tex]\beta + \beta _{6}[/tex] )
∴ 95% confidence interval
-0.43 ± 1.96 * 0.30 = [ -0.43 ± 0.588 ] = ( 0.158 , - 1.018 ) ( hence confidence interval at 95% = 1.96 )
ii) Construct a 95% confidence interval ( between Juanita and Jennifer )
Juanita is a student from the south and Jennifer is a student from Midwest
therefore the difference in expected earnings can be computed as
( [tex]X_{6,A} - X_{5,C} ) = \beta _{0} + \beta _{6} - ( \beta _{0} - \beta _{5} ) = \beta _{6} - \beta _{5}[/tex]
therefore a 95% confidence interval can be calculated with the above regression model.
Find the value of x for ABCD is a parallelogram
Find parallelogram ABCD attached
Answer:
x = 3
Step-by-step explanation:
In parallelograms, the diagonals typically divide each other into 2 equal parts.
This means that from the attached parallelogram, we can say that;
4x - 6 = 2x or 6x - 15 = x
Thus;
4x - 2x = 6
2x = 6
x = 6/2
x = 3
Let's confirm with the second equation;
6x - x = 15
5x = 15
x = 15/5
x = 3
What is the circumference of the circle below? Use 3.14 for π.
Answer:
78.5
Step-by-step explanation:
.....ur welcome.........
3.14×5²
Answer:
C. 31.4
Step-by-step explanation:
To find circumference, you need to use πd. Or just pi times whatever the circumference is. Hope this helped you!!!
PLEASE HELP !! ILL GIVE BRAINLIEST !! 100 POINTS
Answer:
third option
Step-by-step explanation:
How many is it all together
PLEASE HELP- VKLFNJOF:L
Answer:
−4m + 10
Step-by-step explanation:
Combine Like Terms:
= 6m + 10 + −10m
= (6m+−10m) + (10)
= −4m + 10
Hope it helped.
Which of the following functions is NOT a linear function?
A y = 5
B
y == 5x
C y = 5(x - 2)
D y == 5x – 2 + x?
A. y = 5, is the correct answer.
B, C, D are all able to form into the y = mx + b equation, so it's not correct. A is not able to form that equation, therefore, A is correct. Hope that helps :)
a = 8: b = ; C = 10.
Answer:
b=6
[tex]a^{2} + b^{2} = c^{2} \\ {8}^{2} + {b}^{2} = {10}^{2} \\ 64 + {b}^{2} = 100 \\ 100 - 64 = {b}^{2} \\ 36 = {b}^{2} \\ \sqrt{36} = \sqrt{ {b}^{2} } \\ 6 = b[/tex]
Create an inequality to describe the possible values for the total area, A, in square feet of your green section.
The Area of triangle represented using inequality is A ≤ 48.67 [tex]ft^{2}[/tex].
What is Area of triangle?
The area of a triangle is half the product of its base and height.
i.e., Area of triangle= [tex]\frac{1}{2} * b* h[/tex]
Given, b= 6.2 feet and h= 15.7 feet
Area of triangle= [tex]\frac{1}{2} * b* h[/tex]
= 0.5 x 6.2 x 15.7
= 48.67 [tex]ft^{2}[/tex]
The inequality will be: Area of triangle, A≤ 48.67 [tex]ft^{2}[/tex]
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is anyone good with Vertex Angles? i need help
Answer:
t=5
Step-by-step explanation:
Vertical angles are congruent
So we put the value equivalent to each other
110=4t+90
Isolate t
110=4t+90
-90 -90
20=4t
Divide to isolate t
20/4=4t/4
5=t