apply the distributive property
[tex]4x-3=x+9[/tex]apply the substraction property
4. The pair of events that is non-mutually exclusive is A. Turning over an odd number and turning over an even number B. Turning over a prime number and turning over a perfect square C. Turning over a one-digit number and turning over a two-digit number D. Turning over a multiple of 2 and turning over a multiple of 7 5. A student draws one card at random from a standard deck of 52 playing cards. The probability that the card is a diamond or a face card is A. 0.058 B. 0.077 C. 0.423 D. 0.481 Use the following information to answer the next question. On any particular Saturday evening, the probability that Hannah will go 1 to the movies and go for a coffee is The probability that she will go
In one deck we have Spades, Clubs, Hearts, and Diamonds. Each one has 13 cards and 3 face cards. So the let's do this step by step. The probability to get a diamond card is:
[tex]P(diamond)\text{ = }\frac{13}{52}[/tex](13 diamond cards in a total of 52). Then the probability to get a face card is:
[tex]P(facecard)\text{ = }\frac{12}{52}[/tex](12 face cards in a total of 52). We have to sum these probabilities but also we have to subtract the possibilities that include a card that is a face card and diamond (because if we don't do that we are going to count these cards two times). This probability is:
[tex]P(DiamondandFaceCard)\text{ = }\frac{3}{52}[/tex](We have only 3 cards in the deck that are diamond and face cards). Therefore, the probability will be:
[tex]\text{Probability = P(diamond) + P(facecard) - P(Diamond and Face Card)}[/tex][tex]\text{Probability = }\frac{13}{52}\text{ + }\frac{12}{52}\text{ - }\frac{3}{52}[/tex][tex]\text{Probability = }0.423[/tex]Suppose f(x)= 2+4x^2.Simplify as much as possible: f(1)/f(2)= ______
Given,
The expression is,
[tex]f(x)=4x^2+2[/tex]Taking x =1,
Subsituting the value of x in the given function then,
[tex]\begin{gathered} f(1)=4(1)^2+2 \\ =4\times1+2 \\ =4+2 \\ =6 \end{gathered}[/tex]Taking x =2,
Subsituting the value of x in the given function then,
[tex]\begin{gathered} f(2)=4(2)^2+2 \\ =4\times4+2 \\ =16+2 \\ =18 \end{gathered}[/tex]Divide f(1) by f(2) then,
[tex]\frac{f(1)}{f(2)}=\frac{6}{18}=\frac{1}{3}[/tex]Hence, the simplified value is 1/3.
If the probability of an event is what is the probability of the event not happening?20/69Write your answer as a simplified fraction.
If an event has a probability P of happening, then there is a probability of (1-P) of the event not happening.
In this case the probability of the event is p=20/69.
Then, the probability of the event not happening is:
[tex]P(\text{not happening})=1-p=1-\frac{20}{69}=\frac{69-20}{69}=\frac{49}{69}[/tex]Answer: the probability of the event not happening is 49/69.
who can solve this for me it's due next class period
Here, we want to get the value of x
As we can see, we have the interior angle as 45;
The other is 90; and that means the last angle will be 45
This mean that we have an isosceles right-triangle
The sides that face the angles are equal
These sides are x and 12
That means x = 12
To get the value of y, we have to use the Pythagoras' theorem
The square of the hypotenuse (the longest side and the side that faces the right angle) is equal to the sum of the squares of the two other sides
The side facing the right angle is y
So, the sum of the squares of x and 12 will give the square of y
Mathematically, we have this as follows;
[tex]\begin{gathered} y^2=12^2+x^2 \\ \sin ce\text{ x = 12} \\ y^2=12^2+12^2 \\ y^2\text{ = 144 + 144} \\ y^2\text{ = 288} \\ y\text{ = }\sqrt[]{288} \\ y\text{ = 12}\sqrt[]{\text{ 2}} \end{gathered}[/tex]I get 15 percent discount at a store if I find a I like for 40 how much will I have to pay for it
price: $40
Given that you get a 15% discount, you get a discount of $40*15% = $6.
Then, you have to pay $40 - $6 = $34
Write an inequality for the problem and answer the question about the inequality. The square of x is greater than or equal to 10. Is 3 a solution.
"The square of x..." translates to x²
"...is greater than or equal to 10." translates to ≥ 10.
To determine if 3 is a solution, substitute 3 to the inequality.
[tex]\begin{gathered} x^2\ge10 \\ \text{If }x=3 \\ (3)^2\ge10 \\ 9\ge10 \\ 9\ngeq10 \end{gathered}[/tex]The resulting number, 9 is not greater than 10. Therefore, 3 is not a solution.
Joanna is wrapping a present in the box shown.find the amount of wrapping paper in square inches that Joanna needs
First we need to convert 1 ft to inches
1ft= 12 in
We will use the formula of surface area
[tex]SA=2lw+2lh+2wh[/tex]where l is the length, w is the width and h is the height
In our case
l=12 in
w=8in
h=6 in
we substitute
[tex]SA=2(12)(8)+2(12)(6)+2(8)(6)[/tex]we simplify
[tex]SA=432\text{ in}^2[/tex]She needs 432 square inches
The picture that I sent to the app would not pick up the greater or less than signs. The instructions say solve the system of inequalities by graphing. I would like someone to walk me through the steps. I had an amazing tutor the last time but my connection got lost she sent me a graph to help me.
See graph below
Explanation:We have two inequalities:
y < 6
y > x + 3
To plot the inequalities on a graph, we change the inequality sign to equal to in order to get points to plot the graph:
y = 6
This means at y = 6, there will be an horizontal line for all values of x. But due to the less than sign, it means the horizontal line will be shaded down.
y = x + 3
We assign values to x inorder to get y values:
let x = -2, 0, 2, 4
when x = -2
y = -2 + 3 = 1
when x = 0
y = 0 + 3 = 3
when x = 2
y = 2 +3 = 5
when x = 4
y = 4 + 3 = 7
When we plot this points, we get a straight line. SInce the sign is greater than, the line will be shaded towards the positive side
plotting the graph:
First inequality
Both inequalities:
Evaluate the expression when a =3 and x = - 5-8a + x
We have an expression:
[tex]-8a+x[/tex]We have to evaluate it when a = 3 and x = -5. To do that we replace a and x by its values and calculate:
[tex]\begin{gathered} -8(3)+(-5) \\ -24-5 \\ -29 \end{gathered}[/tex]Answer: the expression value is -29
A. Find the domain of f(x). Write your answer in interval notation.B. Find the range of f(x). Write your answer in interval notation.C. Find the following:i. f(0)ii. f(-2)iii. f(8)iv. f(3)V. fl-1)D. Find all x's (approximately) such that f(x)=1.
A) D = [-8, 5) U [-4, -1) U (-1, 3] U (3, 5) U [6,8]
B) R =(-7,-5) U (-4,5] U [6, 7]
C)
i. f(0) = 1
ii. f(-2) = 1
iii. f(8) = 7
iv. f(3) = 4
D.
x= 1,
x= -2
x= -4
x = -7.7 (approximately)
A) Examining the graph, we can write the Domain (the set of entries) as:
D = [-8, 5) U [-4, -1) U (-1, 3] U (3, 5) U [6,8]
Note that as we're dealing with the Real Set there are infinite values within each interval. And the Domain is the union of all intervals.
B) Examining that, for the Range (Outputs) y-axis, we can write the following:
R =(-7,-5) U (-4,5] U [6, 7]
Note that as there are some discontinuities we can't write them as a unique interval.
C) For this item, let's find out each value by locating the y-coordinate on the graph when the value of x is within the parentheses:
i. f(0) = 1 When x = 0, y = 1
ii. f(-2) = 1
iii. f(8) = 7
iv. f(3) = 4
Note that for this value, we have an open dot for -5 so it does not include it
v. f(-1) = Undefined
Both open dots
D. When f(x) = 1, i.e. y= 1 we have the following x-coordinates:
x= 1,
x= -2
x= -4
x = -7.7 (approximately)
Solve for a 76=4/5a+16
Answer:
a=75
Step-by-step explanation:
76=4/5a+16
first get the a term by itself on one side
76-16=4/5a
simplify
60=4/5a
now divide both sides by 4/5 or multiply by 5/4(its the same thing)
60*5/4=4/5a*5/4
now simplify
75=a
One number is five more than three times another. If their sum is increased by one, the result is twenty-six. Find the numbers.The smaller of the numbers is ? and the larger is ? .
Let:
x = The smaller number
y = The larger number
[tex]y=3x+5_{\text{ }}(1)[/tex][tex]x+y+1=26_{\text{ }}(2)[/tex]Replace (1) into (2):
[tex]x+3x+5+1=26[/tex]Add like terms:
[tex]4x+6=26[/tex]Solve for x:
[tex]\begin{gathered} 4x=26-6 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Replace x into (1):
[tex]\begin{gathered} y=3(5)+5 \\ y=20 \end{gathered}[/tex]Answer:
The smaller number is 5
The larger number is 20
You invested $5000 between two accounts paying 7% and 8% annual interest. If the total interest earned for the year was $380, how much was invested at each rate?
Let x be the amount invested in the account paying 7% and y the amount invested in the account paying 8%, then we can set the following system of equations:
[tex]\begin{gathered} x+y=5000 \\ 0.07x+0.08y=380 \end{gathered}[/tex]Solving the first equation for x and substituting it in the second equation we get:
[tex]0.07(5000-y)+0.08y=380[/tex]Solving for y we get:
[tex]\begin{gathered} 350-0.07y+0.08y=380 \\ 0.01y=30 \\ y=3000 \end{gathered}[/tex]Substituting y=3000 in the first equation and solving for x we get:
[tex]\begin{gathered} x+3000=5000 \\ x=2000 \end{gathered}[/tex]Therefore, $2000 was invested in the account paying 7%, and $3000 was invested in the account paying 8%.
select the point(s) of the x intercept of the function shown below
ANSWER:
(-1, 0) and (3, 0)
STEP-BY-STEP EXPLANATION:
The x-intercept is the points where the graph crosses the x-axis, we can calculate it graphically like this:
Help with this question please!!What are the coordinates of the vertex?
The coordinates of the vertex are:
[tex](-2,-4)[/tex]8 people have to give a presentation in class today. How many different orders can theyspeak in?65,5364,09640,32013,440
Answer:
They can speak in 40, 320 different orders
Explanation:
Given that 8 people have to give a presentation in class.
They can speak in many different orders:
First could be second, second could be first, third could be eight, seventh could be fifth, and so on.
This number of ways result in factorial 8.
This is written as:
[tex]8![/tex]Which represents the multiplications of numbers on the number line from 8 down to 1.
That is:
[tex]\begin{gathered} 8!=8\times7\times6\times5\times4\times3\times2\times1 \\ \\ =40,320 \end{gathered}[/tex]Find the value of c using the given chord and secant lengths in the diagram shown to right . c= (Round to the nearest tenth as needed .)
ANSWER
c = 6.4
EXPLANATION
The intersecting chords theorem says that the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment.
One secant segment is (9+19) and its external segment is 9. The other is (13+c) and its external segment is 13:
[tex]9\cdot(9+19)=13\cdot(13+c)[/tex]Solving for c:
[tex]\begin{gathered} 9\cdot28=13^2+13c \\ 252=169+13c \\ 252-169=13c \\ 83=13c \\ c=\frac{83}{13} \\ c=6.3846\ldots \\ c\approx6.4 \end{gathered}[/tex]determine whether the equation below has a one solutions,no solutions, or an infinite number of solutions. afterwards, determine two values of x that support your conclusion.x-4=4-x
x - 4 = 4 - x
4 is subtracting on the left, then it will add on the right
x is subtracting on the right, then it will add on the left.
x + x = 4 + 4
2x = 8
2 is multiplying on the left, then it will divide on the right
x = 8/2
x = 4
So, there is only one solution
Consider the functions f(x)=4-X^2 and g(x)=3x+5.Find the value of f(g)g-2))).
Solution
First find the g(x)
g(-2)= 3(-2) +5
g(-2)= -6+5
g(-2)= -1
substitute for x in f(x) when x is -1
[tex]\begin{gathered} F(-1)=4-(-1)^2 \\ F(-1)\text{ = 4-1} \\ F(-1)\text{ =3} \end{gathered}[/tex]The correct option is the last option
a shop sells on average 250 can's of juice a day there are 25500 cans in stock how many days will these stocks last
If a shop sells on average 250 can's of juice a day and there are 25500 cans, these stocks last for 102 days
A shop sells on average 250 can's of juice a day, it has, it has 25500 cans in stock. We need to find the number of days these stocks will last.
The number of days can be found by using unitary method
1 can of juice is being sold in 1/250 day
25500 can of juice will be sold in 1/250 (25500)
25500 can of juice will be sold in 102 days
Therefore, if a shop sells on average 250 can's of juice a day and there are 25500 cans, these stocks last for 102 days.
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c-884= -853solve for c
c-884= -853
solve for c
that means Isolate the variable c
so
step 1
Adds 884 both sides
c-884+884=-853+884
simplify
c=31Mrs. Peck is making school supply baskets. She purchased 27 composition booksand 9 packs of map pencils. Which shows the ratio of packs of map pencils tocomposition books.
Number of composition books: 27
Number of packs of map pencils: 9
The ratio of packs of maps pencils to composition books: 9 to 27
9/27 = 1/3
1:3
Which expression fits this description? • The expression is the quotient of two quantities. • The numerator of the expression is the product of 5 and the sum of x and y. • The denominator is the product of negative 8 and x. 5x + y 5(x + y) - (8 + x) 5x + y –8+x 5(x + y) -82 - 8x Done -
Given the word problem:
The numerator of the expression is the product of 5 and the sum of x and y and The denominator is the product of negative 8 and x.
The numerator will be the value on top in a fraction.
Here, the numerator is the product of 5 and the sum of x and y ==> 5(x + y)
The denominator is the value below in a fraction.
Here, the denominator is the product of negative 8 and x ==> -8x
Therefore, the expression that fits this description is:
[tex]\frac{5(x+y)}{-8x}[/tex]14. What property is used to show that 3(4-6) = 12-18?
Answer:
Distribution property method
The rectangular foor of a classrom is 30 feet in length and 24 feet in width. A scale drawing of the floor has a length of 5 inches. What is the perimeter, in inches, of the floor in the scale drawing?
The required perimeter of the scale drawing is given as 18 inches.
Given that,
The rectangular floor of a classroom is 30 feet in length and 24 feet in width. A scale drawing of the floor has a length of 5 inches. The perimeter, in inches, of the floor in the scale drawing, is to be determined.
Perimeter is the measure of the figure on its circumference.
Here,
According to the question,
L = 30 feet, W = 24 feet,
for Scaled drawing
l = 5 inch, w = x
Now,
30/5 = 24 / x
6 = 24 / x
x = 24 {1/6}
x = 4,
So the width of the scale drawing is 4 inches,
perimeter of the scaled drawing = 2[l + w]
= 2 [5 + 4] = 18 inches
Thus, the required perimeter of the scale drawing is given as 18 inches.
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solve Equation: 4(x-6)=76
We have the next equation
[tex]4(x-6)=76[/tex][tex]\begin{gathered} x-6=\frac{76}{4} \\ x-6=19 \\ x=19+6 \\ x=25 \end{gathered}[/tex]4. Look at the figures below.How was each point of Polygon ABCDE shifted to get Polygon BCDE?A right I unit and down 4 unitsBright I unit and down 1 unitC. left 1 unit and up 4 unitsD. left I unit and up 1 unitTi
Given a polygon ABCDE with the coordinates
[tex]A(-7,2),B(-8,4),C(-6,5),D(-5,6),E(-5,3)[/tex]The image of the polygon has vertices A'B'C'D'E' with coordinates
[tex]A^{\prime}(-6,-2),B^{\prime}(-7,0),C^{\prime}(-5,1),D^{\prime}(-4,2),E^{\prime}(-4,-1)[/tex]The transformation rule as observed from the image is
[tex](x,y)\Rightarrow(x+1,y-4)[/tex]Hence, the polygon has been shifted to the right by 1 unit and down by 4 units
Option A is the right answer
suppose you want to subtract: -4-(-2)
SOLUTION
To answer this question, let us first understand some rules that guide operations as this:
[tex]\begin{gathered} -\times-=+ \\ -\times+=- \\ +\times+=+ \\ +\times-=- \end{gathered}[/tex]So going back to treat this question:
[tex]-4-(-2)[/tex]Re-writing this subtraction as an ADDITION of signed numbers, we will have:
[tex]\begin{gathered} -4-(-2) \\ =-4+2 \end{gathered}[/tex]Now to complete this problem the final solution will result in:
[tex]\begin{gathered} =-4+2 \\ =-2 \end{gathered}[/tex]The final answer is -2
Find the distance between the points (2, – 5) and ( – 7, – 7)
Answer:
=[tex] \sqrt{85} [/tex]
Step-by-step explanation:
let, (x1,y1) = (2,-5) & (x2,y2) = (-7,-7)
now, for distance between two points,
D = [tex]\sqrt[]{(x_{1}-x_{2} )^{2} +(y_{1}-y_{2} )^{2} }[/tex]
=[tex]\sqrt[]{(2-(-7))^{2}+(-5-(-7))^2 }[/tex]
[tex]=\sqrt{(2+7)^2+(-5+7)^2}[/tex]
[tex]=\sqrt{9^2+2^2}[/tex]
[tex]=\sqrt{81+4}[/tex]
[tex]=\sqrt{85}[/tex]
Answer:
[tex] \huge{ \boxed{ \sqrt{85} \: \text{or} \: 9.219 \: \text{units}}}[/tex]
Step-by-step explanation:
The distance between two points say [tex] A(x_1,y_1) [/tex] and B(x_2,y_2) can be found by using the formula;
[tex] \bold{d = \sqrt{{x_2-x_1}^{2}+{y_2-y_1}^{2}}} [/tex]
From the question the points are (2, – 5) and ( – 7, – 7)
[tex] x_1=2 \\ y_1=-5 \\ x_2=-7 \\ y_2=-7 [/tex]
Substituting the values into the formula that is;
[tex]d = \sqrt{ {( - 7 - 2)}^{2} + {( - 5 - - 7)}^{2} } \\ d = \sqrt{ {( - 9)}^{2} + {(2)}^{2} } \\ d = \sqrt{81 + 4} \\ d = \sqrt{85} = 9.219[/tex]
We have the final answer as
√85 or 9.219 unitsG is located at (0, 4)What are the coordinates of G' after G undergoes the translation (x,y)-> (x-5,y+2)?
Applying the translation rule:
G(0, 4) → (0-5, 4+2) → G'(-5, 6)