Given any three numbers a, b, and c.
By the distributive law, we must have:
a x (b + c) = (a x b) + (a x c)
Now to find 8 x78
8 x 78 = 8 x (70 + 8) = (8 x 70) + (8 x 8) = 560 + 64 = 624
use prowers and multiplication to write the equation whose value is 10 to the 11th power
if we have
(10^9)(10^2)
adds the exponents
10^(9+2)
10^11
If you have
10^18/ 10^7
subtract the exponents
10^(18-7)
10^11
If you have
(10^6)^2/10
First multiply the exponents
10^(6*2)/10
10^12/10
subtract exponents
10^(12-1)
10^11
The Following to wait table shows the number of student of the school who have a cell phone and or part-time job:
Explanation
in the column we have
-have cell phones
-do not have cell phones
-total
and
in the other side.
-have a part time job
-do not have part time job,
so to know the number of students whoh fit both conditions ( have a cell phone and have a part time job) we need to find the cell where both intersect each other
hence, the answer is
[tex]2)40[/tex]I hope this helps you
Consider the following quadratic function Part 3 of 6: Find the x-intercepts. Express it in ordered pairs.Part 4 of 6: Find the y-intercept. Express it in ordered pair.Part 5 of 6: Determine 2 points of the parabola other than the vertex and x, y intercepts.Part 6 of 6: Graph the function
Answer:
The line of symmetry is x = -3
Explanation:
Given a quadratic function, we know that the graph is a parabola. The general form of a parabola is:
[tex]y=ax^2+bx+c[/tex]The line of symmetry coincides with the x-axis of the vertex. To find the x-coordinate of the vertex, we can use the formula:
[tex]x_v=-\frac{b}{2a}[/tex]In this problem, we have:
[tex]y=-x^2-6x-13[/tex]Then:
a = -1
b = -6
We write now:
[tex]x_v=-\frac{-6}{2(-1)}=-\frac{-6}{-2}=-\frac{6}{2}=-3[/tex]Part 3:For this part, we need to find the x-intercepts. This is, when y = 0:
[tex]-x^2-6x-13=0[/tex]To solve this, we can use the quadratic formula:
[tex]x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot(-1)\cdot(-13)}}{2(-1)}[/tex]And solve:
[tex]x_{1,2}=\frac{6\pm\sqrt{36-52}}{-2}[/tex][tex]x_{1,2}=\frac{-6\pm\sqrt{-16}}{2}[/tex]Since there is no solution to the square root of a negative number, the function does not have any x-intercept. The correct option is ZERO x-intercepts.
Part 4:
To find the y intercept, we need to find the value of y when x = 0:
[tex]y=-0^2-6\cdot0-13=-13[/tex]The y-intercept is at (0, -13)
Part 5:
Now we need to find two points in the parabola. Let-s evaluate the function when x = 1 and x = -1:
[tex]x=1\Rightarrow y=-1^2-6\cdot1-13=-1-6-13=-20[/tex][tex]x=-1\Rightarrow y=-(-1)^2-6\cdot(-1)-13=-1+6-13=-8[/tex]The two points are:
(1, -20)
(-1, -8)
Part 6:
Now, we can use 3 points to find the graph of the parabola.
We can locate (1, -20) and (-1, -8)
The third could be the vertex. We need to find the y-coordinate of the vertex. We know that the x-coordinate of the vertex is x = -3
Then, y-coordinate of the vertex is:
[tex]y=-(-3)^2-6(-3)-13=-9+18-13=-4[/tex]The third point we can use is (-3, -4)
Now we can locate them in the cartesian plane:
And that's enough to get the full graph:
The function g is defined as follows for the domain given g(x) = 3x - 2 , omain = \{- 2, - 1, 0, 1\} Write the range of g using set notation. Then graph g
Given: The function below
[tex]\begin{gathered} g(x)=3x-2 \\ Domain:\lbrace-2,-1,-0,1\rbrace \end{gathered}[/tex]To Determine: The range and the graph of g
Solution
The range is as given below
[tex]\begin{gathered} x=-2 \\ g(-2)=3(-2)-2=-6-2=-8 \\ x=-1 \\ g(-1)=3(-1)-2=-3-2=-5 \end{gathered}[/tex][tex]\begin{gathered} x=0 \\ g(0)=3(0)-2=0-2=-2 \\ x=1 \\ g(1)=3(1)-2=3-2=1 \end{gathered}[/tex]Hence, the range is
{-8, -5, -2, 1}
Let us form a table showing the domain(x) and the range (g(x))
Let us use the table to plot graph of the domain(x) against the range(g(x)) as below
Issac says that T' will be located at (4,20)Isabella says that T' will be located at (4,12(who is correct and why?
In the given triangle :
The coordinate of T is ( 2, 10 )
Triangle TUV will be dilated by a scale factor of 2
Thus, multiply the coordinates of TUV by 2
T' = 2 x T
T' = 2 x ( 2, 10 )
T' = ( 2x2, 2x10)
T' = ( 4, 20 )
So, T' will be located at ( 4, 20 )
Issac says that T' will be located at (4,20)
Answer : Issac says that T' will be located at (4,20)
Hey can you please help me with this question and please may sure the answer correctly
Option C is the answer
Write this trinomial in factored form. 5a² - 30 - 14
replace x with a for this exercise
we use this formula to factor
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a=5, b=-3 and c=-14
[tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(5)(-14)}}{2(5)}[/tex][tex]\begin{gathered} x=\frac{3\pm\sqrt[]{9+280}}{10} \\ \\ x=\frac{3\pm\sqrt[]{289}}{10} \\ \\ x=\frac{3\pm17}{10} \end{gathered}[/tex]we have two roots
[tex]\begin{gathered} x=\frac{3+17}{10} \\ x=2 \end{gathered}[/tex]and
[tex]\begin{gathered} x=\frac{3-17}{10} \\ \\ x=-\frac{7}{5} \end{gathered}[/tex]so the simplified equation is
[tex](x-2)(x+\frac{7}{5})[/tex]now replace x for a
[tex](a-2)(a+\frac{7}{5})[/tex]the remainder when f(x)is divided by x-3 is 15. Does f(-3) =15? explain why or why not
We will see that the function f(x) is:
f(x) = 15*(x - 3)
Evaluating it in x = -3 we can see that:
f(-3) = -90
Is the statement true?We know that when we divide f(x) by (x - 3), the quotient is 15. (that is the statement given in the question)
so we can write the equation:
f(x)/(x - 3) = 15
And we can solve this for f(x) as if it were a variable, then we get:
f(x) = 15*(x - 3)
Now, if we evaluate the function in x = -3 (this is replacing the variable x with the number -3), we will get:
f(-3) = 15*(-3 - 3) = 15*(-6) = -90
So the statement:
f(-3) = 15
Is false
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Given:• UZ | VW• UV ZUZ306Nw4511Which is closest to mZW?26.630°60°63.49
From the image, given that UZ is parallel to VW, UV is congruent to UZ. We can redraw the image to include some extra details.
The image is below;
With the image above, we can the find the angle W, using tangent function of trigonometry.
This is seen below;
[tex]\begin{gathered} \tan w=\frac{opposite}{\text{Adjacent}} \\ \text{opposite =30ft} \\ \text{Adjacent}=15ft \\ \therefore\tan w=\frac{30}{15} \\ \tan w=2 \\ w=\tan ^{-1}2 \\ w=63.4^0 \end{gathered}[/tex]The angle closest to m
Answer: 63.4
how do i expand -4(-x-8)
Answer:
4x+32
Step-by-step explanation:
mutiply the -4 to both numbers inside parentheses. negative * negative= positive. -4*-x=4x, -4*-8=32
Jamie had 10 dogs. She killed 4 of them then bought another 3. She also ate 7 of them. How many dogs dose she have now?
Answer:
2 dogs
Step-by-step explanation:
10-4+3-7
6-4
2
Answer: 2 dogs
Step-by-step explanation:
QUESTION WHO KILLS AND EATS DOGS?????
What is the length of the dotted line in the diagram below? Round to the
nearest tenth.
Answer:
12.1 units
Step-by-step explanation:
Tyler said he swam 23 tenths miles this week. His coach said Tyler swam 2.3 miles this week. To find who is correct, model the distance both Tyler and his coach said Tyler swam. Use the flat as 1 unit. A: What do you need to use?B: What do you know about representing whole numbers and decimals that may help you solve the problem? C: Complete the sentencesAre the models alike or different?Tyler swam _____ tenths, or _____, miles.So, _____________________ are correct.
Answer with explanation:
We need to determine if what Tyler is saying is in fact equal to what his coach said, to get the final answer, we have to concert the resulting units in miles:
Taylor's answer:
[tex]23\times(\frac{1}{10})\text{ miles}\Rightarrow(\frac{23}{10})\text{miles}\Rightarrow2.3\text{ miles}[/tex]Coach's answer:
[tex]2.3\text{ miles}[/tex]In conclusion, The two answers are correct so the two models are indeed alike.
Write the following ratio using two other notations: 1/3
Given:
[tex]\frac{1}{3}[/tex]To write the given fraction into two other notations, we use "to" for word notation while ":" for number notation.
Therefore, the answers are:
1 to 3
1:3
choose the correct letter ( this is not being graded it is review )
we have the points
(-2,6) and (-3,-7)
step 1
Find out the slope
m=(-7-6)/(-3+2)
m=-13/-1
m=13
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=13
point (-2,6)
substitute and solve for b
6=13(-2)+b
6=-26+b
b=32
therefore
y=13x+32
step 3
Convert to standard form
AX+By=C
y=13x+32
13x-y=-32 -------> is equivalent to -13x+y=32
therefore
the answer is option Dis 6x0=O and example of distributive property?
we have that
Distributive property is the product of a factor and a sum (or difference) equals the sum (or difference) of the product
In this exanple
6x*0=0
Is not the product of a factor and a sum or difference
Graph a line that contains the point 2 (-5, -6) and has a slope of 3 Y 6 4 2 2 -6 -4 2 4 6 -4- -6-
the graph of a line passing through point
[tex](x_1,y_1)[/tex]with gradient m
is given by
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y+6=3(x+5) \\ \Rightarrow y+6=3x+15 \\ \Rightarrow y=3x+9 \end{gathered}[/tex]Allen's goal is to have between 1,500 and 1,600 bottles in his collection. Write and solve a compound inequality to determine the number of weeks it will take Allen to reach his goal.
The compound inequality is 1500 < 300 + 25x < 1600, the solution is 48 < x < 52 and the number of weeks to reach his goal 48 to 52 weeks
How to determine the compound inequality?The given parameters from the question are
Existing collection = 300
Rate = 25 bottles each week
Represent the number of weeks by x and the total number of bottles with y
So, we have the following equation
y = Existing collection + Rate * x
This gives
y = 300 + 25x
Also, we have
The goal is to have between 1,500 and 1,600 bottles in his collection.
This means that
1500 < Total < 1600
So, we have
1500 < 300 + 25x < 1600
Evaluate the like terms
1200 < 25x < 1300
Divide by 25
48 < x < 52
Hence, the number of weeks is 48 to 52 weeks
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Possible question
Allen wants to add to his existing collection of 300 bottles. Starting today, he will collect 25 bottles each week.
Allen's goal is to have between 1,500 and 1,600 bottles in his collection. Write and solve a compound inequality to determine the number of weeks it will take Allen to reach his goal.
Patient Smith was on a diet. He weighed 122.6 kilograms. After one month he weighed 112.8 kilograms. Whatwas his total weight loss in one month?
If Smith uses both medications, then its dosage is the sum of each.
[tex]\text{total dosage = 48.5 + 0.5 = 4}9\text{ ml}[/tex]The total dosage of the medication would be 49 ml if he got both medications.
2x^3-16x^2-40x=0 factor
The given expression is
[tex]2x^3-16x^2-40x=0[/tex]We extract the common factor 2x.
[tex]\begin{gathered} 2x(x^2-8x-20)=0 \\ 2x=0\rightarrow x=0 \\ x^2-8x-20=0 \end{gathered}[/tex]The first solution is 0.
Now, we solve the quadratic expression. We have to find two numbers whose product 20 and whose difference is 8. Those numbers are 10 and 2.
[tex]x^2-8x-20=(x-10)(x+2)[/tex]Hence, the given expressions expressed, as factors, is[tex]2x^3-16x^2-40x=x(x-10)(x+2)[/tex]I’ve done all the other parts, I simply need you to graph the proabola!
Given
[tex]y=x^2-4x+3[/tex]Find
Graph the parabola of the given function
Explanation
[tex]y=x^2-4x+3[/tex]solve the equation
[tex]\begin{gathered} x^2-4x+3=0 \\ x^2-3x-x+3=0 \\ x(x-3)-(x-3)=0 \\ (x-1)(x-3)=0 \\ x=1,3 \end{gathered}[/tex]vertex can be found by using the formula,
[tex]-\frac{b}{2a}=-\frac{-4}{2}=2[/tex]x = 2 , substitute this in equation to get y value,
y = -1
if x = 0 then y =3 and if y= 0 then x = 1, 3
Final Answer
Solve these: state whether there is no solution, one solution specify it , or infinitely many Solutions.
Step 1:
Write the two systems of equations
y = 3x = 2
3x = y - 3
Step 2:
Substitute y from the first equation into the second equation
[tex]\begin{gathered} 3x\text{ = y - 3} \\ 3x\text{ = 3x + 2 - 3} \\ 3x\text{ - 3x = 2 - 3} \\ 0\text{ = 2 - 3} \\ 2\text{ = 3} \end{gathered}[/tex]Final answer
NO SOLUTION
P(B) = 2/3P(An B) = 1/6What will P(A) have to be for A and B to be independent?1/211/121/45/6
P(B) = 2/3
P(An B) = 1/6
What will P(A) have to be for A and B to be independent?
Remember that
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true
substitute given values
1/6=P(A)*(2/3)
solve for P(A)
P(A)=1/4A plane intersects both bases of a cylinder, passing through the center of each baseof the cylinder. What geometric figure will be formed from this intersection?
When a plane intersects both bases of a cylinder, passing through the center of each base of the cylinder, the cross section formed is a rectangle.
Bentley has 32 biscuits left in his treat jar. If this represents 4/5 of what he orginally had in the jar, how may treats did he have in the beginning
he had 40 biscuits in the beginning
Explanation
to solve this we can use a rule of three
so
Step 1
let x represents the total treats he had in the beginning , so
[tex]\begin{gathered} if \\ 32\text{ biscuits}\rightarrow\frac{4}{5}of\text{ total } \\ then \\ x\text{ biscuits}\rightarrow total\text{ \lparen1\rparen} \end{gathered}[/tex]so, the proportion is
[tex]\begin{gathered} \frac{32}{\frac{4}{5}\text{ }}=\frac{x}{1} \\ \frac{160}{4}=x \\ x=40 \end{gathered}[/tex]therefore,
he had 40 biscuits in the beginning
I hope this helps you
A class had a quiz where scores ranged from 0 to 10.N(s) models the number of students whose score on the quiz was s.What does the statement N(8) > N(5) mean?Group of answer choicesA score of 8 is greater than a score of 5.There are more students who scored 8 than students who scored 5.There are 8 students who scored higher than 5.
The expression N(s) models the number of students that got a score "s" on the quiz.
Then the expression N(8) represents the number of students that scored 8 on the quiz.
And N(5) represents the number of students that scored 5 on the quiz.
[tex]N(8)>N(5)[/tex]Can be read as: "The number of students whose score on the quiz was 8 is greater than the number of students whose score on the quiz was 5"
Therefore, you can conclude that there were more students who scored 8 than students who scored 5. (option 2)
two factor of 2=2²two factor of 3=3²
Exponents indicate how many times a number is multiplied by itself
Two factor two= 2*2= 2²=4
Two factor of three is 3*3=3²=9
For a period of d days an account balance can be modeled by f(d) = d^ 3 -2d^2 -8d +3 when was the balance $38
Given a modelled account balance for the period of d days as shown below:
[tex]\begin{gathered} f(d)=d^3-2d^2-8d+3 \\ \text{where,} \\ f(d)\text{ is the account balance} \\ d\text{ is the number of days} \end{gathered}[/tex]Given that the account balance is $38, we would calculate the number of days by substituting for f(d) = 38 in the modelled equation as shown below:
[tex]\begin{gathered} 38=d^3-2d^2-8d+3 \\ d^3-2d^2-8d+3-38=0 \\ d^3-2d^2-8d-35=0 \end{gathered}[/tex]Since all coefficients of the variable d from degree 3 to 1 are integers, we would apply apply the Rational Zeros Theorem.
The trailing coefficient (coefficient of the constant term) is −35.
Find its factors (with plus and minus): ±1,±5,±7,±35. These are the possible values for dthat would give the zeros of the equation
Lets input x= 5
[tex]\begin{gathered} 5^3-2(5)^2-8(5)-35=0 \\ 125-2(25)-40-35=0 \\ 125-50-75=0 \\ 125-125=0 \\ 0=0 \end{gathered}[/tex]Since, x= 5 is a zero, then x-5 is a factor.
[tex]\begin{gathered} d^3-2d^2-8d-35=(d-5)(d^2+3d+7)=0 \\ (d-5)(d^2+3d+7)=0 \\ d-5=0,d^2+3d+7=0 \\ d=0, \end{gathered}[/tex][tex]\begin{gathered} \text{simplifying } \\ d^2+3d+7\text{ would give} \\ d=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=1,b=3,c=7 \end{gathered}[/tex][tex]\begin{gathered} d=\frac{-3\pm\sqrt[]{3^2-4\times1\times7}}{2\times1} \\ d=\frac{-3\pm\sqrt[]{9-28}}{2} \\ d=\frac{-3\pm\sqrt[]{-17}}{2} \end{gathered}[/tex]It can be observed that the roots of the equation would give one real root and two complex roots
Therefore,
[tex]d=5,d=\frac{-3\pm\sqrt[]{-17}}{2}[/tex]Since number of days cannot a complex number, hence, the number of days that would give a balance of $38 is 5 days
What do the following two equations represent?y-3=2(x - 3)y+5 = 2(x + 1) a. the same lineb. distinct parallel linesc. perpendicular linesd. intersecting, b it not perpendicular
Option A: The same line
Explanations:The slope-intercept form of the equation of a line can be written as:
y = mx + c
Where m is the slope
and c is the intercept
Let us express the two equations given in the slope-intercept form
For the first equation:
y - 3 = 2(x - 3)
y - 3 = 2x - 6
y = 2x - 6 + 3
y = 2x - 3
The slope, m = 2
The intercept, c = -3
For the second equation:
y + 5 = 2(x + 1)
y + 5 = 2x + 2
y = 2x + 2 - 5
y = 2x - 3
We can see that both equations simplify to y = 2x - 3, this means the both equations represent the same line
A decorator creates a scale drawing of a dinning room table. The length of the scale is 3 centimeters. The image represents the dimensions of the actual dinning room table. What is the area of the scale drawing?
From the image given, the dinning room table is a rectangle.
Given:
Length in inches = 90 inches
Width in inches = 45 inches
The scale of the length is 3 centimeters.
Now, let's find the scale of the table:
[tex]\frac{90}{3}=30\text{inches}[/tex]This means that 30 inches represents 1 centimeter.
Also, let's find the width in centimeters:
[tex]\frac{45}{30}=1.5\operatorname{cm}[/tex]Thus, we have:
Length of scale drawing = 3 cm
Width of scale = 1.5 cm
To find the Area of the scale drawing, use the area of a rectangle:
A = Length x Width
[tex]A=3\times1.5=4.5\operatorname{cm}^2[/tex]Therefore, the length of the scale drwing is = 4.5 cm²
ANSWER:
[tex]4.5\operatorname{cm}^2[/tex]