Answer:
[tex]x = -\frac{3}{2}[/tex] or [tex]x = 1[/tex]
Step-by-step explanation:
Using the zero product property, first step is to set the given equation, [tex] 2x^2 + x - 1 = 2 [/tex] , to zero. Then factorise the left side.
Thus,
[tex] 2x^2 + x - 1 = 2 [/tex]
Subtract 2 from both sides
[tex] 2x^2 + x - 1 - 2 = 2 - 2 [/tex]
[tex] 2x^2 + x - 3 = 0 [/tex]
Factorise the left side
[tex] 2x^2 + 3x - 2x - 3 = 0 [/tex]
[tex] x(2x + 3) - 1(2x + 3) = 0 [/tex]
[tex] (x - 1)(2x + 3) = 0 [/tex]
Find the solution
[tex] x - 1 = 0 [/tex]
Or
[tex]2x + 3 = 0[/tex]
[tex] x = 1 [/tex]
Or
[tex]2x + 3 = 0[/tex]
[tex]2x = -3[/tex]
[tex]x = -\frac{3}{2}[/tex]
The answer is: [tex] x = 1 [/tex] or [tex]x = -\frac{3}{2}[/tex]
5(y–3.8)=4.7(y–4) help help
Answer:
y = 2/3 or 0.667Step-by-step explanation:
5(y–3.8)=4.7(y–4)
Expand the terms in the bracket
That's
5y - 19 = 4.7y - 18.8
Group like terms
5y - 4.7y = 19 - 18.8
0.3y = 0.2
Divide both sides by 0.3
We have the final answer as
y = 2/3 or 0.667Hope this helps you
Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many hours did Ronald spend on his homework?
Answer:
Step-by-step explanation:
½ of 5¼
½×(21/4)
=21/8
=2⅝ hours
Answer:
2 5/8
Step-by-step explanation:
you would divide 5 1/4 by 2 :
5 divided by 2 =2 1/2
1/4 divided by 2=1/8
then make the numbers have the same denomanator
1/2, 2/4, 4/8
1/8,
then you add
2 4/8+1/8=2 5/8
A department store offers two promotions. Promotion A says, "Buy one pair of shoes, get the second pair for half the price." Promotion B says, "Buy one pair of shoes, get $10 off the second pair." Jane wants to buy two pairs of shoes that cost $30 each. She can only use one of the promotions, A or B. Jane decides to use the promotion that will save her the most money. How many dollars does Jane save by picking one promotion over the other? (For example, if Jane spends $150 on her purchase by using one promotion and $100 on her purchase by using the other promotion, she saves $150-100=50$ dollars by using the second promotion over the first.)
Answer:
$5
Step-by-step explanation:
Using Promotion A, Jane would buy the first pair for $30 and the second for 1/2 * 30 = $15 for a total of 30 + 15 = $45. Using Promotion B, she would buy the first pair for $30 and the second for 30 - 10 = $20 for a total of 30 + 20 = $50. Since 45 < 50, Promotion A is the better deal, so Jane would save 50 - 45 = $5.
At Jefferson Middle School, eighty-two students were asked which sports they plan to participate in for the coming year. Twenty students plan to participate in track and cross country; six students in cross country and basketball; and eight students in track and basketball. Twelve students plan to participate in all three sports. A total of thirty students plan to participate in basketball, and a total of forty students plan to participate in cross country. Ten students don't plan to participate in any of the three sports. How many students plan to just participate in cross country? 2 4 40 30
Answer:
40
Step-by-step explanation:
In the question only lies the answer:
"and a total of forty students plan to participate in cross country."
Answer:
2
Step-by-step explanation:
2
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = - 1/2x
B.
y = 1/2x
C.
y = 2x
D.
y = -6x
E.
y = 6x
F.
y = 3x
Answer:
y=-6x
Step-by-step explanation:
square root of 49/64 answered as a fraction
Answer:
Hey there!
That would be 7/8
Let me know if this helps :)
If the area of the square is A(s) = s², find the formula for the area as a function of time, and then determine A(s(3)).
A(t) = 100t^2 + 500t + 625
3,025 square pixels
Answer:
A(t) equals 100t²+ 500t + 625.
The area of the square image after 3 seconds is 3,025 square pixels.
Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answer:
15x - y = - 126
Step-by-step explanation:
will make it simple and short
first we need to find the slope (m) first in order to get the equation
given: (-8,6) (-9,-9)
y2 - y1 -9 - 6
Slope = m = ----------- = ------------------ = 15
-x2 - x1 -9 - (-8)
so the equation of the line using point (-8,6) and slope 15 is y - 6 = 15( x + 8)
y - 6 = 15x + 120
using the form equation Ax + By = C, 15x - y = -120-6
therefore... 15x - y = - 126 is the answer
area please it's easy plzzzzzzzzzz
a ) Now as you can see, the white region is composed of a triangle and a rectangle. This triangle has a height of 5, as it is composed of the respective blank triangles. It's base is 5 meters as well, by properties of a rectangle - which is sufficient information to solve for the area of the triangle.
Area of Triangle : 1 / 2 [tex]*[/tex] 4 [tex]*[/tex] 5 = 2 [tex]*[/tex] 5 = 10 m²
The area of this rectangle will be 3 [tex]*[/tex] 4 = 12 m², considering it's given dimensions are 3 by 4. Therefore the area of this white region will be 10 + 12 = 22 m²
b ) Now this striped region will be the remaining area, or the area of the white region subtracted from the area of the outer rectangle.
Area of Outer Rectangle : 10 [tex]*[/tex] 4 = 40 m²,
Area of Striped Region : 40 - 22 = 18 m²
Complete each equation with a number that makes it true. 5⋅______=15 4⋅______=32 6⋅______=9 12⋅______=3
Answer: blank 1: 3 Blank 2: 8 blank 3: 1.5 blank 4: 0.25
Step-by-step explanation:
5 times 8=15
4 times 8=32
6 times 1.5=9
12 times 0.25=3
The complete equation is
5⋅____3__=15
4⋅___8___=32
6⋅___1.5___=9
12⋅__0.25____=3
What is Multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.
Multiplication Formula
The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:
Multiplicand: The first number (factor).Multiplier: The second number (factor).Product: The final result after multiplying the multiplicand and multiplier.Multiplication symbol: '×' (which connects the entire expression)5 * 3=154 * 8=326 * 1.5=912 * 0.25=3Learn more about multiplication here:
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Find the measure of F. A. 44 B. 88 C. 90 D. 46
Answer:
A. 44º
Step-by-step explanation:
The sum of internal angles in a triangle is equal to 180 degrees, whereas the sum for a square is equal to 360 degrees. Given that three triangles depicted on figure constructs a square, it is to conclude that each is an isosceles triangle. The following relations are presented:
1) [tex]e + 92^{\circ} = 180^{\circ}[/tex] Given
2) [tex]a = b[/tex], [tex]c = d[/tex] Given
3) [tex]a + b + 92^{\circ} = 180^{\circ}[/tex] Given.
4) [tex]c + d + e = 180^{\circ}[/tex] Given.
5) [tex]b + c = 90^{\circ}[/tex] Given.
6) [tex]2\cdot a + 92^{\circ} = 180^{\circ}[/tex] 2) in 3)
7) [tex]a = 44^{\circ}[/tex] Algebra
8) [tex]b = 44^{\circ}[/tex] By 2)
9) [tex]b= f[/tex] Alternate internior angles.
10) [tex]f = 44^{\circ}[/tex] By 8). Result
Hence, the answer is A.
A spinner has five congruent sections, one each of blue, green, red, orange, and yellow. Yuri spins the spinner 10 times and records his results in the table. A 2-column table has 5 rows. The first column is labeled Color with entries blue, green, red, orange, yellow. The second column is labeled Number with entries 1, 2, 0, 4, 3. Which statements are true about Yuri’s experiment? Select three options. The theoretical probability of spinning any one of the five colors is 20%. The experimental probability of spinning blue is One-fifth. The theoretical probability of spinning green is equal to the experimental probability of spinning green. The experimental probability of spinning yellow is less than the theoretical probability of spinning yellow. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.
Answer:
A. The theoretical probability of spinning any one of the five colors is 20%.
C. The theoretical probability of spinning green is equal to the experimental probability of spinning green.
E. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.
These are the answers on edg 2020, just took the test.
Step-by-step explanation:
Answer:
a, c, e,
Step-by-step explanation:
:)
Simplify 70 +(-30)+2+(-9)+0.3+(-0.1)=[70+(-30)] +[2+(-9)]+[0.3+(-0.1)]
Answer:
Step-by-step explanation:
When you add the left side of the equation, you get 33.2 because 70-30 is 40, 40+2 is 42, 42-9 is 33, 33+0.3 is 33.03, 33.3-0.1 is 33.2.
When you add the right side of the equation, you get 33.2, because they are the same problem but on side has brackets.
Hope this helps you.
2/5(10c -35) (the 35 is negative)
Answer:
The simplified form is 2 (c - 7).
Step-by-step explanation:
The expression to be solved is:
[tex]f (c)=\frac{2}{5} (10c -35)[/tex]
Simplify the expression as follows:
[tex]f (c)=\frac{2}{5} (10c -35)[/tex]
[tex]=[\frac{2}{5}\times 10c]-[\frac{2}{5}\times 35]\\\\=[2\times 2c]-[2\times 7]\\\\=4c-14\\\\=2(c-7)[/tex]
Thus, the simplified form is 2 (c - 7).
football team, won 35 out of 39 games over a period of 4 years. if they keep winning pace, predict how many games you would expect them to win over the next 78 football games
Answer:
70
Step-by-step explanation:
If the team continues with same pace, they expected wins as per previous ratio:
35/39*78 = 70Expected wins 70 out of 78 games
Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major: Accounting 83 Management 68 Marketing 85 Economics 64 Total 300 Has there been any significant change in the number of students in each major between the last school year and this school year?
Answer:
There has been no significant change in the number of students in each major between the last school year and this school year.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: There has been no change in the number of students.
Hₐ: There has been a significant change in the number of students.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
Here,
[tex]O_{i}[/tex] = Observed frequencies
[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.
The chi-square test statistic value is, 1.662.
The degrees of freedom is:
df = 4 - 1 = 4 - 1 = 3
Compute the p-value as follows:
[tex]p-value=P(\chi^{2}_{k-1} >1.662) =P(\chi^{2}_{3} >1.662) =0.645[/tex]
*Use a Chi-square table.
The p-value is 0.645.
The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.
Thus, it can be concluded that the there has been no significant change in the number of students in each major between the last school year and this school year.
Suppose 65% of people in Georgia support a special transportation tax. Alejandro is not confident that this claim is correct. To investigate the claim, he surveys 150 people in his community and discovers that 78 people support a special transportation tax.
A. calculate sample proportion.
B. calculate standard error of the sample proportion, (SE). Give answer to three decimal places
C. Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.
Answer:
C
Step-by-step explanation:
Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.
A. The sample proportion is 0.52.
B. The standard error of the sample proportion is approximately 0.041.
C. The standard error of the sample proportion estimate is approximately 0.041.
A. To calculate the sample proportion, we divide the number of people who support the special transportation tax (78) by the total number of people surveyed (150):
Sample proportion = 78 / 150 = 0.52
B. To calculate the standard error of the sample proportion (SE), we use the formula:
[tex]SE = \sqrt{(p * (1 - p)) / n}[/tex]
where p is the sample proportion and n is the sample size. Substituting the values into the formula:
[tex]SE = \sqrt{(0.52 * (1 - 0.52)) / 150}\\\\SE = \sqrt{0.2496 / 150}\\\\SE = \sqrt{0.001664}\\\\SE = 0.0407[/tex]
Therefore, the standard error of the sample proportion is approximately 0.041 (rounded to three decimal places).
C. The standard error of the sample proportion estimate (SEest) is the same as the standard error of the sample proportion (SE) calculated in part B. Hence, the standard error of the sample proportion estimate is also approximately 0.041 (rounded to three decimal places).
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50q + 43 > −11q + 70
Answer:
q > 27/61
Step-by-step explanation:
50q + 43 > −11q + 70
Add 11 q to each side
50q+11q + 43 > −11q+11q + 70
61q+43> 70
Subtract 43 from each side
61q> 27
Divide each side by 61
61q/61> 27/61
q > 27/61
A caplet contains 325 mg of medication. How many caplets contain 975 mg of medication?
Answer:
3 capletsStep-by-step explanation:
Given 1 caplet = 325 mg of medication, to calculate the number of caplet 975mg of medication will contain, we will follow the steps below;
Let 1 caplet = 325 mg of medication
x caplet = 975 mg of medication
Cross multiply
325 * x = 1 * 975
325x = 975
Divide both sides by 325
325x/325 = 975/325
x = 3
Hence 3 caplets contains 975 mg of medication.
g If the events A and B are independent with P( A) = 0.35 and P( B) = 0.45, then the probability that both events will occur simultaneously is:
Answer:
0.1575.
Step-by-step explanation:
Here, as they are independent, we multiply the probabilities:
P( A and B) = 0.35*0.45
= 0.1575.
The probability that both events will occur simultaneously is 0.1575.
Given that, the events A and B are independent with P( A) = 0.35 and P( B) = 0.45.
What is independent probability?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).
Since, the events A and B are independent
We have P(A and B)
= P(A) × P(B)
= 0.35 × 0.45
= 0.1575
Hence, the probability that both events will occur simultaneously is 0.1575.
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3.85∙47.3+52.7∙3.85 PLSSSSS HELP
Answer:
385
Step-by-step explanation:
Find an equation of the plane through the point(1, 5,-1) and perpendicular to the vector (1, 5, 1). Do this problem in the standard way.
Answer:
x+5y+z = 25Step-by-step explanation:
Given a plane passing through the point(1, 5,-1) and perpendicular to the vector (1, 5, 1), the equation of the plane can be expressed generally as;
a(x-x₀)+b(y-y₀)+c(z-z₀) = 0 where (x₀, y₀, z₀) is the point on the plane and (a, b,c) is the normal vector perpendicular to the plane i.e (1,5,1)
Given the point P (1, 5, -1) and the normal vector n(1, 5, 1)
x₀ = 1, y₀ =5, z₀ = -1, a = 1, b = 5 and c = 1
Substituting this point in the formula we will have;
a(x-x₀)+b(y-y₀)+c(z-z₀) = 0
1(x-1)+5(y-5)+1(z-(-1)) = 0
(x-1)+5(y-5)+(z+1) = 0
x-1+5y-25+z+1 = 0
x+5y+z-1-25+1 = 0
x+5y+z-25 = 0
x+5y+z = 25
The final expression gives the equation of the plane.
Which of the following is the graph of the quadratic parent function
This is the graph of y = x^2. It is a parabola that opens upward and has its vertex at the origin. Applying various transformations to the parent function will allow us to produce any parabolic graph we want. In effect, the parent function is like the most basic building block.
The graph of the function f(x) = (x − 3)(x + 1) is shown.
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0).
Which describes all of the values for which the graph is positive and decreasing?
all real values of x where x < −1
all real values of x where x < 1
all real values of x where 1 < x < 3
all real values of x where x > 3
Answer:
x < -1
Step-by-step explanation:
Since the parabola opens upward, it is positive and decreasing where the left branch is above the x-axis: all points to the left of x=-1.
all real values of x where x < -1
Calculate, correct to one decimal plice
the acute angle between the lines
3x - 4y + 5 = 0 and 2x + 3y -1 = 0
A. 70.69
B. 50.2
C. 39.8
D. 19.4
Answer:
A. 70.69 is the correct answer.
Step-by-step explanation:
Given:
Two lines:
[tex]3x - 4y + 5 = 0 \\2x + 3y -1 = 0[/tex]
To find:
Angle between the two lines = ?
Solution:
Acute Angle between two lines can be found by using the below formula:
[tex]tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|[/tex]
Where [tex]\theta[/tex] is the acute angle between two lines.
[tex]m_1, m_2[/tex] are the slopes of two lines.
Slope of a line represented by [tex]ax+by+c=0[/tex] is given as:
[tex]m = -\dfrac{a}{b }[/tex]
So,
[tex]m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}[/tex]
[tex]m_2 = -\dfrac{2}{ 3}[/tex]
Putting the values in the formula:
[tex]tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}[/tex]
So, correct answer is A. 70.69
log 7 (x^2 + 11) = log 7 15
Answer:
x = ±2
Step-by-step explanation:
log 7 (x^2 + 11) = log 7 15
We know that log a ( b) = log a(c) means b =c
x^2 + 11 = 15
Subtract 11 from each side
x^2 = 15-11
x^2 =4
Take the square root of each side
sqrt(x^2) =±sqrt(4)
x = ±2
Cases Prudence has a special (cubic) die. The values on its face are the integers from 1 to 6, but they are not arranged ae in a normal die. When Prudence first tosses the die, the sum of the values on the four side faces is 15. In her second toss, the sum of these values is 12. Find what value appears in the face opposite 6 on Prudence’s special die. (Hint: what are possible values for the top and bottom face when the sum of the side faces is 12).
Answer: 3
Step-by-step explanation:
first, we know that:
1 + 2 + 3 + 4 +5 +6 = 21
Now, which two numbers we should take out in order to have 15?
we can remove the 2 and the 4, or the 1 and the 5.
so here we have two possibilities, 2 and 4 are opposite, or 1 and 5 are opposite (they are located in opposite faces of the die)
in the other arrange, we have that removing two numbers we should get 12.
in order to reach 12, we should remove two numbers that add 9 together.
those can be 4 and 5, or 6 and 3.
Now, notice that in the first restriction we have that:
Or 2 and 4 are opposite,
or 1 and 5 are opposite.
So 4 and 5 can never be opposite, so we should have that 6 and 3 are opposite.
Then we can affirm that the value that appears in the face opposite to the 6, is the 3.
10 points plssssss!!!
Answer:
A. rectangle
B. any of triangle, quadrilateral, pentagon, hexagon
Step-by-step explanation:
A. A plane perpendicular to the base will intersect 2 adjacent or 2 opposite lateral faces, as well as the two bases. Each plane intersected will result in an edge of the cross sectional figure. The figure will have two pairs of parallel edges, so is a rectangle.
__
B. If the intersecting plane is not constrained to be perpendicular to the base(s), it can intersect 3, 4, 5, or all 6 faces of the prism. Hence, the shape of the cross section can be any of ...
trianglequadrilateralpentagonhexagonwhich terms are like terms in the following expression ? 6x + 8xy - 3x + 9y + 4x^2
Answer:
[tex]\Large \boxed{{6x \ \mathrm{and} \ -3x}}[/tex]
Step-by-step explanation:
Like terms have identical variables and exponents, the coefficients don’t have to be the same.
The like terms from the expression are 6x and -3x.
Step-by-step explanation:
Hey, there!!
6x and -3x are like terms.
Like terms in algebraic terms are those terms which has same variable or exponents. In This expression "6x+8xy-3x+9y4x^2"
6x and -3x has "x" common in them so, The answer is 6x and -3x.
Hope it helps..
the box plots shows the price for two different brands of shoes
Answer:
A. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25.
Step-by-step explanation:
The most appropriate measure that can be used to compare the SPREAD of the data of the 2 brands plotted on a box plot, is the Interquartile range (IQR).
Interquartile range is the difference between Q3 and Q1.
Q3 is the value which lies at the end of the rectangular box, while the Q1 lies at the beginning of the box.
From the box plot given,
IQR for brand A = 80 - 70 = $10
IQR for brand B = 50 - 25 = $25
Therefore, the correct option is "A. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25."