Answer:
4x+32
Step-by-step explanation:
mutiply the -4 to both numbers inside parentheses. negative * negative= positive. -4*-x=4x, -4*-8=32
Which ordered pair is in the solution set fit the system of inequalities shown below?2x-y<3x+2y>-1A. (-2,-1)B. (0,1)C. (1,-2)D.(6,1)
Given the System of Inequalities:
[tex]\begin{cases}2x-y<3 \\ x+2y>-1\end{cases}[/tex]1. Take the first inequality and solve for "y":
[tex]\begin{gathered} -y<2x+3 \\ (-1)(-y)<(-2x+3)(-1) \\ y>2x-3 \\ \end{gathered}[/tex]Notice that direction of the symbol changes, because you had to multiply both sides of the inequality by a negative number.
Now you can identify that the boundary line is:
[tex]y=2x-3[/tex]Since it is written in Slope-Intercept Form, you can identify that its slope is:
[tex]m_1=2[/tex]And its y-intercept is:
[tex]b_1=-3[/tex]Notice that the symbol of the inequality is:
[tex]>[/tex]That indicates that the line is dashed and the shaded region is above the line.
Knowing all this information, you can graph the first inequality on the Coordinate Plane.
2. Apply the same procedure to graph the second inequality. Solving for "y", you get:
[tex]\begin{gathered} 2y>-x-1 \\ \\ y>-\frac{1}{2}x-\frac{1}{2} \end{gathered}[/tex]Notice that the boundary line is:
[tex]y=-\frac{1}{2}x-\frac{1}{2}[/tex]Where:
[tex]\begin{gathered} m_2=-\frac{1}{2} \\ \\ b_2=-\frac{1}{2} \end{gathered}[/tex]Since the symbol is:
[tex]>[/tex]The line is dashed and the shaded region is above the line.
Knowing this, you can graph the second inequality.
3. Look at the graph of the System of Inequalities:
Notice that:
-The black line is the boundary line of the first inequality and the green line is the boundary line of the second inequality.
- The solution of the system is the intersection region. It is the region where the shaded region of the first inequality and the shaded region of the second inequality, intersect.
4. Plot the points given in the options on the graph of the Systems:
5. You can identify that this point is in the intersection region:
[tex](0,1)[/tex]Therefore, it is a solution.
Hence, the answer is: Option B.
Pls help me :( thx ur the best
Answer:
here you go, but when you go to Kumon you should do the work that they give you, it helps in the long run I promise
----from a former Kumon student, now I grade papers for Kumon
Please mark Brainiest
Answers to page 1 -2
1) 1 1/2
2) 1 1/8
3) 32/63
4) 1 3/40
5) 31/60
6) 11/35
7) 11/35
8) 17/20
9) 1 1/24
10) 27/28
11) 5/6
12) 1/4
Answers to page 3-4
1) 13/24
2) 1 2/45
3) 11/20
4) 2/3
5) 4/5
6) 5/21
7) 1 1/35
8) 67/72
9) 52/165
10) 23/36
11) 9/10
12) 5/6
Those are all the answers. btw the slashes are the line between the fractions if u get what I mean. :)
combine like terms
(x+3)+(9+x)
Answer:
[tex]x^{2}[/tex]+12x+27
Step-by-step explanation:
First, you need to distribute. You multiply x by 9 and x, and then multiply 3 by 9 and x, which results in 9x + [tex]x^{2}[/tex] +27 +3x.
Second, you collect like terms. In this case, there is only one like term, which is x. The results of this should be [tex]x^{2}[/tex] + 27 + 11x.
Lastly, reorder the terms properly, and you're done!
Hope this helps.
Create a polynomial of degree 6 that has no real roots. Explain why it has no real roots. Is it possible to have a polynomial with an odd degree that has no real roots? Explain.
Create a polynomial of degree 6 that has no real roots.
y = ( x^2 + 4) ( x^2 +7 ) ( x^2+5)
Multiplying all the terms together
y =x ^6 + 16 x^4 + 83 x^2 + 140
Using the zero product property
0= x^2 +4 x^2+7 =0 x^2 + 5 =0 will each give a complex solution
x^2 = -4 x^2 = -7 x^2 = -5
This means x = 2i or -2i x = i sqrt(7) or -i sqrt(7) x = i sqrt (5) or - i sqrt(5)
These solutions can be in the form a+bi
Therefor it will have no real roots
y = x^6 + 16 x^4 + 83 x^2 + 140 has no real solutions
Complex solutions come in pairs, so an odd degree must have a real solution
Factor 12x² + 19x - 21.O (6x + 7)(2x − 3)—O (4x - 3)(3x + 7)O(6x-7)(2x + 3)(4x + 3)(3x7)
given the expression
[tex]12x^2+19x-21[/tex]we are loking 2 numbers whose multiplication is equal to 12
and other 2 number whose multiplication is equal to 21
the sum of the cross multiplication is equal of 19, as follows
[tex](4x*3x)+((4x*7)+(3x*-3))+(-3*7)[/tex]factor is
[tex]\left(4x-3\right)\left(3x+7\right)[/tex]correct answer option B
The day's high temperature in Detroit, Michigan was recorded as 50°F. Use the formula C=59(F−32) to write 50°F as degrees Celsius.
Given:
The day's high temperature in Detroit, Michigan was recorded as 50°F.
[tex]C=\frac{5}{9}(F-32)[/tex]Required:
To convert the 50°F as degrees Celsius.
Explanation:
Consider
[tex]C=\frac{5}{9}(F-32)[/tex]For F=50,
[tex]\begin{gathered} C=\frac{5}{9}(50-32) \\ \\ =\frac{5}{9}(18) \\ \\ =5\times2 \\ \\ =10\degree C \end{gathered}[/tex]Final Answer:
[tex]C=10\degree C[/tex]Introduction to Probability
The probability of birthday being in July is 1/12.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a numeric value and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is flipping a fair (impartial) coin. The chance of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.
Probability of birthday being in July = 1/12 (12 months in a year)
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what operation helps calculate unit rates and unit prices
Division operation is operation helps calculate unit rates and unit prices.
Division operation -
A rate with 1 as the denominator is referred to as a unit rate. If you have a rate, such as a price per a certain number of items, and the quantity in the denominator is not 1, you can determine the unit rate or price per unit by performing the division operation: numerator divided by denominator.What method do you employ to determine the unit rate?
Simple division of the numerator and denominator yields the unit rate. The outcome tells us how many of the units in the numerator to anticipate for each unit in the denominator.
What in mathematics are rate and unit rate?
A ratio called a rate compares two amounts of DIFFERENT types of UNITS. When expressed as a fraction, a unit rate has a denominator of 1. Divide the rate's numerator and denominator by the denominator to represent the rate as a unit rate.Learn more about Division operation
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Use the graph of 'f' in the figure below to answer the following questions. 1. State the domain and range of 'f'.2. Find the average rate of change of 'f' over the interval [0,6].
The domain of the given function corresponds to:
[tex]\lbrack-4,-2)\cup(-2,6)[/tex]And the range of the function is:
[tex](-2,6)[/tex]The average rate of change of f over the interval [0,6] is:
[tex]\frac{5.5-(-2)}{0-6}=\frac{7.5}{-6}=-\frac{5}{4}=-1.25[/tex]Find du and v. Treat a and n as constants.
Stated that;
[tex]u=x^n[/tex]Then, differentiating u with respect to x using the power rule where n is a constant is;
[tex]\begin{gathered} du=(n\times1)x^{n-1} \\ du=nx^{n-1} \end{gathered}[/tex]Also,
[tex]dv=e^{ax}[/tex]Then, we can find v by integrating, we have;
[tex]\begin{gathered} \int dv=\int e^{ax}dx \\ v=\frac{1}{a}e^{ax} \\ \end{gathered}[/tex]
Isabella earns interest at an annual rate of 10% compounded annually on her savings account. She deposits $2,000 into her account. What is the total amount of money Isabella will have in her account after 2 years? (Use the formula to calculate compound interest: A = P(1 + r)')
As it indicates on the text, compound interest is represented by the following expression:
[tex]\begin{gathered} A=P(1+r)^t \\ \text{where,} \\ A=\text{ Amount} \\ P=\text{ Principal} \\ r=\text{ interest rate in decimal form} \\ t=\text{ time} \end{gathered}[/tex]Then, substituing the information given:
[tex]\begin{gathered} A=2,000(1+0.1)^2 \\ A=2,420 \end{gathered}[/tex]Isabella will have $2,420 after 2 years.
90 minutes for 3 typed pages; 60 minutes for a a typed pages write a proportion for each phrase and solve it
90 minutes for 3 typed pages; 60 minutes for a a typed pages write a proportion for each phrase and solve it
we have that
90/3=60/a
solve for a
a=(60*3)/90
a=2 pagesI need help with this question please help me asap?
Answer
Explanation
• Range (R): the amount between the upper and lower limit.
what is the image of 2,10 after a dilation by a scale factor of 1/2 centered at the origin
A dilation is given by:
[tex](x,y)\rightarrow(kx.ky)[/tex]where k is the scale factor.
In this case we have:
[tex](2,10)\rightarrow(\frac{1}{2}\cdot2,\frac{1}{2}\cdot10)=(1,5)[/tex]Therefore the image is the point:
[tex](1,5)[/tex]960 watts hour per how many watts hour does it consume in 4 days and 6 hours
Answer:
Explanation:
[tex]undefined[/tex]Find the perimeter of the rectangle. Write your answer in scientific notation.Area = 5.612 times 10^14 cm squared9.2 times 10^7cm is one side of the perimeter
Answer: Perimeter = 1.962 x 10^8 cm
Explanation:
The first step is to calculate the width of the rectangle. Recall,
Area = length x width
width = Area /length
From the information given,
Area = 5.612 times 10^14 cm squared
Length = 9.2 times 10^7cm
Thus,
width = 5.612 times 10^14 /9.2 times 10^7
width = 6.1 x 10^6
The formula for calculating the perimeter is
Perimeter = 2(length + width)
Thus,
Perimeter = 2(9.2 x 10^7 + 6.1 x 10^6)
Perimeter = 1.962 x 10^8 cm
If A and B are supplementary angles and A is nine times as large as B, find the measures of A and B.
Supplementary angles add up to 180°
A+ B = 180
A is 9 times as large as B.
A = 9B
We have the system of equations:
A+ B = 180
A = 9B
Put the second equation into the first one, and solve for B
(9B)+ B = 180
10B = 180
B= 180/10
B = 18
Replace the value of B on any equation and solve for A:
A = 9B
A= 9(18)
A= 162
A= 162°
B=18°
What is the most specific name for each type of special quadrilateral
From the given quadilaterals, let's determine the specific name for each based on the property marked.
• 1a. ,All four sides are marked equal.
Since all four sides are equal, we can say the specific name for the quadilateral is a Square.
A square is a quadilateral with four equal sides.
• 1b. In this quadilateral, we have one pair of parallel sides.
Given that the quadilateral is NOT drawn to scale, the quadilatral here can be said to be a Trapezoid.
A trapezoid is a quadilateral with one pair of parallel side.
• 1c. In this quadilateral, all four angles are marked as right angles.
Given that all four angles are right angles, the specific name for the quadilateral is a Rectangle.
A rectangle is a quadilateral with four interior right angles.
ANSWER:
• 1a. Square
,• 1b. Trapezoid
,• 1c. Rectangle.
In 1990, the cost of tuition at a large Midwestern university was $104 per credit hour. In 1998, tuition had risen to $184 per credit hour.
We have to find the linear relationship for the cost of tuition in function of the year after 1990.
The cost in 1990 was $104, so we can represent this as the point (0, 104).
The cost in 1998 was $184, so the point is (8, 184).
We then can calculate the slope as:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{184-104}{8-0} \\ m=\frac{80}{8} \\ m=10 \end{gathered}[/tex]We can write the equation in slope-point form using the slope m = 10 and the point (0,104):
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-104=10(x-0) \\ y=10x+104 \end{gathered}[/tex]We can then write the cost c as:
[tex]c=10x+104[/tex]We then can estimate the cost for year 2002 by calculating c(x) for x = 12, because 2002 is 12 years after 1990.
We can calculate it as:
[tex]\begin{gathered} c=10(12)+104 \\ c=120+104 \\ c=224 \end{gathered}[/tex]Now we have to calculate in which year the tuition cost will be c = 254. We can find x as:
[tex]\begin{gathered} c=254 \\ 10x+104=254 \\ 10x=254-104 \\ 10x=150 \\ x=\frac{150}{10} \\ x=15 \end{gathered}[/tex]As x = 15, it correspond to year 1990+15 = 2005.
Answer:
a) c = 10x + 104
b) $224
c) year 2005.
Which expression represents the area of the rectangle below in square units
Area of rectangle is given by:-
[tex]\begin{gathered} l\times b \\ =(3x+2)\times2x \\ =6x^2+4x \end{gathered}[/tex]So the correct answer is
[tex]6x^2+4x[/tex]Find the length of AC
The rule of the length of an arc is
[tex]L=\frac{x}{360}\times2\pi\text{ r}[/tex]Where L is the length of the arc
x is the central angle subtended by the arc
r is the radius of the circle
∵ BC = r
∵ BC = 16 ft
∴ r = 16
∵ < ABC is a central angle subtended by the arc AC
∴ ∵ < ABC = 51 degrees
∴ x = 51
→ Substitute the values of x and r in the rule above to find The length of arc AC
[tex]\begin{gathered} AC=\frac{51}{360}\times2\times3.14\times16 \\ AC=14.23466667 \end{gathered}[/tex]→ Round it to 2 decimal places
∴ AC arc = 14.23 ft
f(x) = 3x² - 5x+20
Find f(-8)
Answer:
Substitute x = -8 into f(x).
f(-8) = 3(-8)² - 5(-8) + 20
= 3(64) + 40 + 20
= 192 + 60
= 252
HELP ASAP!!!
Find the square of 1-4i.
ANSAWER:
−15+8i
Explanation:
First, you can expand the square of the bynomial:
NO LINKS!! Please help me with this probability question 2a
====================================================
Work Shown:
A = he eats pizza
B = he drinks cola
P(A) = 0.40
P(B) = 0.60
P(A and B) = 0.30
Then apply the conditional probability formula.
P(A given B) = P(A and B)/P(B)
P(A given B) = 0.30/0.60
P(A given B) = 0.5 exactly
P(A given B) = 50%
If we know for certain he drinks cola, then there's a 50% chance of him eating pizza.
In class, we determined that 11 peoplewould fit comfortably in a 5 ft by 5 ftsquare. How many square feet wouldeach person require?
We have to first determine the area of the square. The area of a square can be represented as follows
[tex]\begin{gathered} \text{Area of square = L}^2 \\ L\text{ = 5 ft} \\ \text{Area of square = 5}^2 \\ \text{Area of a square = 25 ft}^2 \end{gathered}[/tex]The number of each square feet each person will requre can be calculated as follows
[tex]\begin{gathered} numbers\text{ of each square ft each person require = 25/11} \\ numbers\text{ of each square ft each person require = }2.27272727273ft^2 \\ numbers\text{ of each square ft each person require }\approx\text{ }2.27ft^2 \end{gathered}[/tex]A student sketched some art on an 8-inch x 10-inch piece of paper. She wants to resize it to fit a 4-inch x 6 inchframe (as shown below).What percent of the original sketch was still able to be included in the frame?
So,
The area of art can be found multiplying:
8in * 10in = 80in²
And, the area of the frame, can be also found multiplying the dimentions:
4in * 6in = 24in².
If we divide, we'll obtain a ratio between the area of the frame and the area of the art as follows:
[tex]\frac{24}{80}=0.3[/tex]And, 0.3*100% = 30%.
So,30 percent of the original sketch was still able to be included in the frame.
Find the area of the shapes below. Must show all steps includingformula and units! If needed, round your answer to the nearest tenth. This is a parallelogram
Answer: Area = 120 cm^2
Explanation:
The formula for calculating the area of a parallelogram is expressed as
Area = base x height
From the information given,
base = 15
height = 8
Area = 15 x 8
Area = 120 cm^2
4x-6a(8x)/98y Solve for x
1) Solving for x, the following equation:
We're going to isolate the x variable on the left:
[tex]4x-6a\frac{8x}{98y}[/tex]What is the value of x? A pair of intersecting lines is shown. The angle above the point of intersection is labeled left parenthesis 7 x minus 8 right parenthesis degrees. The angle directly opposite below the point of intersection is labeled left parenthesis 6 x plus 11 right parenthesis degrees. (1 point)
A –19
B 125
C 19
D 55
The value of x in the angles is 19.
How to find angles in intersecting lines?When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.
Therefore, let's find the value of x in the intersecting lines.
Hence,
7x - 8 = 6x + 11 (vertically opposite angles)
Vertically opposite angles are congruent and they share the same vertex point.
Hence,
7x - 8 = 6x + 11
subtract 6x from both sides of the equation
7x - 8 = 6x + 11
7x - 6x - 8 = 6x - 6x + 11
x - 8 = 11
add 8 to both sides of the equation
x - 8 + 8 = 11 + 8
x = 19
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a coyote can run a hundred one in 5.3 seconds a jack-rabbit can run 75 m in 4.7 seconds compared their unit speeds to determine which animal is faster round to the nearest whole unit Blank#1 Coyote speedBlank#2 Jack Rabbit speedBlank#3 Which one is faster
Answer
Coyote's speed = 19 m/s
Jack Rabbit's speed = 16 m/s
The Coyote is faster since 19 > 16.
Explanation
To answer this, we need to note that the relationship between speed, distance and time is given as
Speed = (Distance/Time)
For the Coyote,
Distance = 101 m
Time = 5.3 seconds
Speed = (Distance/Time)
Coyote's speed = (101/5.3) = 19 m/s
For the Jack Rabbit,
Distance = 75 m
Time = 4.7 seconds
Speed = (Distance/Time)
Jack Rabbit's speed = (75/4.7) = 16 m/s
Since 19 m/s is evidently greater than 16 m/s, we can conclude that the Coyote is faster than the Jack Rabbit.
Hope this Helps!!!
