to determine the lcm of 6 and 8, express these numbers as the product of prime numbers:
6 = 2x3
8 = 2x2x2
the same factors determine the lcm. In this case, the factors
7+8=15 how do you decompose 10?I'm doing this for my granddaughter she's in the first grade and the teacher wants to know her dude examples 7 + 8 equals 15 and they want her to decompose it to make 10 then and use the number bond to show how you took two
To decompose 10 on basis of 8 it becomes 10 -2 =8
so 8 + 2 =10
can I take a pictureSolve:8^8 / 8^3
Since both bases are equal (8) to divide we have to subtract the exponents:
[tex]8^{(8-3)}[/tex][tex]8^5[/tex]Select ALL the true statements1 poClare created Figure A Then she created Figure B by translating Triangle C and thentranslating Triangle D.Figure AFigureсDFigure A is congruent to Figure BFigure B is a translation of Figure A.Triangle Cis congruent to Triangle CTriangle D'is congruent to Triangle D.
The first statement cannot be true since the complete figure is not the same and sides cannot be overlapped together and look the same without a translation.
The second statement is not true either because if the full figure was translated it would look the same in another position and this is not the case.
The third and forth statements are true because figures were translated and didn't suffer any expansions or contractions which means that all of its sides must be equal and make them congruent.
THE TOP OF A 20 FT. WATERSLIDEIS 16 FT. ABOVE THE GROUND.HOW FAR FROM THE BASE OF THESTEPS WILL THE GUESTS BE SHOTINTO THE WATER?
Using the given information, we form the following diagram.
To find x we use Pythagorean's Theorem.
[tex]20^2=16^2+x^2[/tex]Then, we solve for x.
[tex]\begin{gathered} 400-256=x^2 \\ x=\sqrt[]{144} \\ x=12 \end{gathered}[/tex]Therefore, the answer is 12 feet.Translate the sentence into an equation:seven less than the product of four and a number is equal to 3use the variable x for the unknown number
Given:
seven less than the product of four and a number is equal to 3
Let the number = x
So, the product of four and a number = 4x
seven less than the product of four and a number will be 4x - 7
so, the expression will be:
4x - 7 = 3
Use this graph of y = 2x2 - 12x + 19 to find the vertex. Decide whether thevertex is a maximum or a minimum point.A. Vertex is a minimum point at (3, 1)B. Vertex is a maximum point at (1,7)C. Vertex is a minimum point at (1,3)D. Vertex is a maximum point at (3,1)
Hello there. To slve this question, we'll have to remembrer some properties about maximum and minimum in a quadratic function.
Given a quadratic function f as follows:
[tex]f(x)=ax^2+bx+c[/tex]We can determine whether or not the vertex is a maximum or minimum by the signal of the leading coefficient a.
If a < 0, the concavity ofthe parabolai is facing down, hence it admits a maximum value at its vertex.
If a > 0, the concavity of the parabola is facing up, hence it admits a minimum value at its vertex.
As a cannot be equal to zero (otherwise we wouldn't have a quadratic equation), we use the coefficients to determine an expression for the coordinates of the vertex.
The vertex is, more generally, located in between the roots of the function.
t is easy to prove, y comlpleting hthe square, that the solutions of the equation
[tex]ax^2+bx+c=0[/tex]are given as
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Taking the arithmetic mean of these values, we get the x-coordinate of the vertex:
[tex]x_V=\dfrac{\dfrac{-b+\sqrt{b^2-4ac}}{2a}+\dfrac{-b-\sqrt{b^2-4ac}}{2a}}{2}=\dfrac{-\dfrac{2b}{2a}}{2}=-\dfrac{b}{2a}[/tex]By evaluating the function at this point, we'll obtain the y-coordinate of the vertex:
[tex]f(x_V)=-\dfrac{b^2-4ac}{4a}[/tex]With this, we can solve this question.
Given the function:
[tex]y=2x^2-12x+19[/tex]First, notice the leadin coefficient is a = 2 , that is positive.
Hence it has a minimum point at its vertex.
To determine these coordinates, we use the other coefficients b = -12 and c = 19.
Plugging the values, we'll get
[tex]x_V=-\dfrac{-12}{2\cdot2}=\dfrac{12}{4}=3[/tex]Plugging ths value in the function, ewe'll get
[tex]y_V=f(x_V)=2\cdot3^2-12\cdot3+19=2\cdot9-36+19=1[/tex]Hence we say that the final answer is
Vertex is a minimum point at (3, 1)
As you can see in the gaph.
If f(x) = 2x^2 - 5 and g(x) = 2x + 1, evaluate f(g(x)) when x = -3
when x = -3
[tex]\begin{gathered} \Rightarrow[2(2\times-3+1)^2]-5 \\ 2[-5]^2-5=45 \end{gathered}[/tex]The final answer is 45
Ricardo Cooks pizza at a restaurant he cooks five Pizza on Wednesday 9 pizzas on Thursday four times as many pizzas on Friday then Thursday complete the equation to show P the total number of Pizza is Ricardo Cooks on Wednesdays Thursdays and Fridays
this is the equation
total number of pizzas = pizzas cooked on Wednesday + pizzas cooked on
thursday + pizzas cooked on friday
total number of pizzas = 5 + 9 + 4(9)
total number of pizzas = 14 + 36
total number of pizzas = 50 This is the result
You Start at (3,0). You move right 2 units and down 2 units. Where do you end
You Start at (3,0). You move right 2 units and down 2 units. Where do you end
we have
1) You Start at (3,0)
2) You move right 2 units and down 2 units
so
the rule is (x,y) ------> (x+2,y-2)
(3,0) ------> (3+2,0-2)
(5,-2)compute the unit rate. round to the nearest hundredth. 226 Miles on 12 gallons
The unit rate of miles per gallon is computed dividing the number of miles and the number of gallons as follows:
[tex]\frac{226\text{ miles}}{12\text{ gallons}}=18.83\frac{\text{miles}}{\text{gallon}}[/tex]What is the slope of the line in the graph?A. 8B. 1/8C. 1/4 D. 4
The slope of a line graph can be found using the formula:
[tex]\begin{gathered} slope\text{ = }\frac{y_2-\text{ y}_1}{x_2-x_1} \\ Where\text{ \lparen x}_1,y_1)\text{ and \lparen x}_2,y_2)\text{ are two points on the line} \end{gathered}[/tex]From the graph, we have the points (0,0) and (8, 2)
Substituting the values into the formula:
[tex]\begin{gathered} slope\text{ = }\frac{2-0}{8-0} \\ =\text{ }\frac{2}{8} \\ =\text{ }\frac{1}{4} \end{gathered}[/tex]Answer:
slope = 1/4 (Option C)
Which group of relatives make 25% of her guest she has 12 cousins 6 aunts 4 brothers 2 sister
From the statement of the problem, we know that the organizer has the following guests:
• 12 cousins,
,• 6 aunts,
,• 4 brothers,
,• 2 sisters.
The total number of guests is 12 + 6 + 4 + 2 = 24. A 25% of the total number of guests is 0.25*24 = 6 guests. Because the group of aunts has 6 members, that group represent 25% of her guest.
Answer
The group of 6 aunts represents 25% of her guests.
Find the equation (in terms of x) of the line through the points (-4,-4) and (3,1)y=
In order to find the equation of the line, first let's calculate its slope m using the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the given points (x1, y1) = (-4, -4) and (x2, y2) = (3, 1), we have:
[tex]m=\frac{1-(-4)}{3-(-4)}=\frac{1+4}{3+4}=\frac{5}{7}[/tex]Now, to find the equation, let's use the slope-intercept form and calculate the value of b using a given point:
[tex]\begin{gathered} y=mx+b \\ (3,1): \\ 1=\frac{5}{7}\cdot3+b \\ 1=\frac{15}{7}+b \\ b=1-\frac{15}{7} \\ b=-\frac{8}{7} \end{gathered}[/tex]Therefore the equation is y = (5/7)x - 8/7
Reshanda bought 17 plants to arrange along the border of her garden. How many distinct arrangements can she make if the plants are comprised of 6 tulips, 5 roses, and 6 daisies?
Given the word problem, we can deduce the following information:
1. Reshanda bought 17 plants to arrange along the border of her garden.
2. The plants are comprised of 6 tulips, 5 roses, and 6 daisies.
To determine the distinct arrangements that can she make, we use permutation as it an arrangement of objects in a definite order. The process is shown below:
[tex]Arrangements=\frac{n!}{p_1!p_2!p_3!}[/tex]where:
n=number of different objects=17
p1=objects of the first kind=6
p2=objects of the second kind=5
p3=objects of the third kind=6
We plug in what we know:
[tex]\begin{gathered} Arrangements=\frac{n!}{(p_{1})!(p_{2})!(p_{3})!} \\ =\frac{17!}{6!5!6!} \\ Calculate \\ Arrangements=5717712 \end{gathered}[/tex]Therefore, the answer is 5717712 arrangements.
The sum of two numbers is 95. If the larger number is increased by twice the smaller number the result is 120 what is the largest number
Let x represent the smaller number
Let y represent the larger number
The sum of the two numbers is 95. This means that
x + y = 95
If the larger number is increased by twice the smaller number, the result is 120. This means that
2x + y = 120
The system of equations representing the word problem is
x + y = 95, 2x + y = 120
use the figure two parallel lines cut by a transvesal.
Answer:
a. 137°
Explanation:
∠1 and ∠8 are corresponding angles. They are in the same relative position with respect to the parallel lines and the transversal.
Then, corresponding angles have the same measure, so:
∠8 = ∠1
∠8 = 43°
Now, ∠8 and ∠6 form a straight line, so the sum of these angles is 180°. Therefore, the measure of ∠6 can be calculated as:
∠6 = 180 - ∠8
∠6 = 180 - 43
∠6 = 137°
So, the answer is a. 137°
what is 2/3 times 3/8
Mutiply both fractions:
[tex]\frac{2}{3}\times\frac{3}{8}[/tex][tex]\frac{2\times3}{3\times8}=\frac{6}{24}[/tex]Simplify by 6.
[tex]\frac{1}{4}[/tex]Answer:
Do the multiplication straight across 2 times 3= 6. 3times 8= 24 so 6/24 or 1/4
An angle measures 24.6° more than the measure of its complementary angle. What is the measure of each angle? _and_
You have two angles, let's call them ∠1 and ∠2 of unknown measure, one of them measures 24.6º more than the other and both angles are complementary.
Let "xº" be the measure of ∠1, then ∠2 will beasure (x+24.6)º
∠1 and ∠2 are complementar, this means that together they add up to 90º
[tex]\angle1+\angle2=90º[/tex]Replace the expression with the angles measures
[tex]x+(x+24.6)=90[/tex]And solve for x
[tex]\begin{gathered} 2x+24.6=90 \\ 2x=90-24.6 \\ 2x=63.6 \\ \frac{2x}{2}=\frac{65.4}{2} \\ x=32.7 \end{gathered}[/tex]The angles measure:
∠1=32.7º
∠2=32.7+24.6=57.3º
Juan has a bag of candy with 20 pieces that are the same shape and size.
40% of the pieces are only chocolate.
20% of the pieces are only caramel.
•The remainder of the pieces are only toffee
Juan eats I piece of caramel candy from the bag and then gives the bag to her friend
Susanna. If Susanna takes one piece of candy from the bag without looking, what is the
probability the piece she takes will be chocolate?
The probability the piece Susanna takes will be chocolate 8/19
Juan has a bag of candy with 20 pieces
40% of the pieces are only chocolate
Number of only chocolate pieces = (40/100) 20 = 8 pieces
20% of the pieces are only caramel.
Number of only charamel pieces = (20/100) 20 = 4 pieces
The remainder of the pieces are only toffee
number of toffee = 20 - 8 - 4 = 8
Juan eats 1 piece of caramel candy from the bag
For Sussana
Now the number of caramel pieces are 3
and the number of candies present = 20 - 1 = 19
probability = number of desired outcomes/ sample space
P(chocolate) = 8/19
Therefore the probability the piece Susanna takes will be chocolate 8/19
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Which of the following shows that f(x) grows at the same rate as g(x)? (5 points)the limit as x goes to infinity of the quotient of f of x and g of x equals 1000the limit as x goes to infinity of the quotient of f of x and g of x equals 0the limit as x goes to infinity of the quotient of f of x and g of x equals infinityNone of these
The function f(x) grows at the same rate as the function g(x) according to the condition : [tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} =1000[/tex].
We are given two functions. The functions are f(x) and g(x). The definitions of the functions are not given explicitly, but we need to find the relationship between the functions. Both functions grow at a certain rate. We need to find the condition that shows that the function f(x) grows at the same rate as the function g(x). The ratio of the limiting values of the two functions must be a finite and non-zero constant for the functions to have the same rate of growth.
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Volume with PI math problem, we are looking at number two. The sentence says, Pam served her apple pie on a 13 inch diameter dish, she wanted to tie a ribbon around the dish to make it a little bit more festive. How long does the ribbon need to be in order to fit around the dish?
81.68 inches
Explanation
Step 1
Let
diameter=13 inches
so, to find the length of the ribbon find the circumference of the pizza
[tex]\text{Circumference}=2\cdot\pi\cdot radius[/tex]Let
radius=13 inches
replace,
[tex]\begin{gathered} \text{Circumference}=2\cdot\pi\cdot radius \\ \text{Circumference}=2\cdot\pi\cdot13\text{ inches} \\ \text{Circumference}=26\pi\text{ inches} \\ \text{Circumference}=81.68\text{ inches} \end{gathered}[/tex]so, the ribbon has to be 81.68 inches
I hope this helps you
I have a calculus question about the definite integral, from my high school AP Calculus Class, pic included
Given the following definite integral.
[tex]\int_{-4}^4\sqrt{4^2-x^2}dx[/tex]We will use the substitution to solve the definite integral
Let the following:
[tex]\begin{gathered} 4sin(\theta)=x \\ 4cos(\theta)*d\theta=dx \\ And: \\ 4^2-x^2=4^2-4^2sin^2\theta=4^2(1-sin^2\theta)=4^2cos^2\theta \end{gathered}[/tex]Substitute into the given integral:
[tex]\begin{gathered} \int_{-4}^4\sqrt{4^2-x^2}dx=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\sqrt{4^2cos^2\theta}*4cos(\theta)*d\theta \\ \\ =\int_{-\pi/2}^{\pi/2}4cos\theta *4cos\theta *d\theta=\int_{-\pi/2}^{\pi/2}16cos^2\theta *d\theta \end{gathered}[/tex]Now, we will use the following identity:
[tex]cos^2\theta=\frac{1}{2}(1+cos2\theta)[/tex]So, the integral will be:
[tex]\begin{gathered} =\int_{-\pi/2}^{\pi/2}\frac{16}{2}(1+cos2\theta)d\theta \\ \\ =8(\theta+\frac{1}{2}sin2\theta) \end{gathered}[/tex]substitute θ = π/2, and θ = -π/2
So, the value of the integral =
[tex]8*(\frac{\pi}{2}-(-\frac{\pi}{2}))=8π[/tex]So, the answer will be: Area = 8π
The graph of the given function is shown in the following picture
HELPPP!!
If Leo gets paid $125 in every paycheck and he immediately puts 50% into his savings account each time. How much money will he put into his savings accounts when he cashes the check?
Answer:
$62.5
Step-by-step explanation
125/2 can be simplified to 62.5/1 or just $62.5
can you show me step by step how to divide 6 1/8 divided by 1 3/4
From the question we are asked to divide 6 1/8 by 1 3/4
To do this, we first convert this improper fraction to proper fraction
6 1/8 = 49/8
1 3/4 = 7/4
The next step is to convert to decimal.
49/8 = 6.125
7/4 = 1.75
So lets divide 6.125 by 1.75
6.125/1.75 = 3.5
Now let's convert the decimal back to fraction
3.5 in fraction = 7/2 = 3 1/2
So, 6 1/8 divide by 1 3/4 = 3 1/2
2×9×5+32+4 Order of operation
2×9×5 + 32 + 4
First, we have to compute the multiplications
2×9×5 = 90
Then,
2×9×5 + 32 + 4 =
= 90 + 32 + 4
Now we only have additions, we can compute them
90 + 32 + 4 = 126
Manuel has a bag of marbles with 2 blue marbles, 1 white marbles, and 1 red marbles.Find the following probabilities of Manuel drawing the given marbles from the bag if the first marble(s) is(are) returned to the bag after they are drawn.a) a blue, then a red b) a red, then white c) a blue, then a blue, then a blue
Explanation
We are given the following:
[tex]\begin{gathered} Bag=\begin{cases}{2\text{ }blue\text{ }marbles} \\ {1\text{ }white\text{ }marbles} \\ {1\text{ }red\text{ }marbles}\end{cases} \\ Total\text{ }marbles=2+1+1=4 \end{gathered}[/tex]We are required to determine the following probabilities:
[tex]\begin{gathered} (a)\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }red \\ (b)\text{ }a\text{ }red,\text{ }then\text{ }white \\ (c)\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }blue \end{gathered}[/tex]We know that probability is calculated as:
[tex]Prob.=\frac{Number\text{ }of\text{ }required\text{ }outcome}{Number\text{ }of\text{ }possible\text{ }or\text{ }total\text{ }outcome}=\frac{n(E)}{n(S)}[/tex]For Question A:
We can determine the probability of a blue, then a red as:
[tex]\begin{gathered} P(blue\text{ }and\text{ }red)=P(Blue)\times P(Red) \\ =\frac{2}{4}\times\frac{1}{4}=\frac{2}{16}=\frac{1}{8} \\ \therefore P(blue\text{ }and\text{ }red)=\frac{1}{8} \end{gathered}[/tex]For Question B:
We can determine the probability of a red, then white as:
[tex]\begin{gathered} P(red\text{ a}nd\text{ w}h\imaginaryI te)=P(Red)\times P(Wh\imaginaryI te) \\ =\frac{1}{4}\times{}\frac{1}{4}=\frac{1}{16} \\ \operatorname{\therefore}P(red\text{ a}nd\text{ w}h\imaginaryI te)=\frac{1}{16} \end{gathered}[/tex]For Question C:
We can determine the probability of a blue, then blue, then blue as:
[tex]\begin{gathered} P(blue,blue,blue)=P(blue)\times P(blue)\times P(blue) \\ =\frac{2}{4}\times\frac{2}{4}\times\frac{2}{4}=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8} \\ \therefore P(blue,blue,blue)=\frac{1}{8} \end{gathered}[/tex]Hence, the answers are:
[tex]\begin{gathered} (a)\text{ }P(blue\text{ }and\text{ }red)=\frac{1}{8} \\ \\ (b)\text{ }P(red\text{ a}nd\text{ w}h\mathrm{i}te)=\frac{1}{16} \\ \\ (c)\text{ }P(blue,blue,blue)=\frac{1}{8} \end{gathered}[/tex]Which congruence theorems can be used to prove AEFG = AJHG? Select two options.
E
H
G
G
F
The options that can help prove that the triangles EFG and JHG are congruent are determined as follows:
Two triangles are said to be congruent (or the same) if:
i) One of the triangles has the lengths of all its sides equal to the lengths of the sides of the other triangle.
This scenario is called the SSS scenario
ii) One of the triangles has the lengths of two of its sides equal to the lengths of two sides of the other triangle, and then both of the two triangles have an angle in common.
This scenario is called the SAS scenario
From the above explanations, we can tell that the two triangles EFG and JHG will be congruent under the scenarios SAS and SSS
Thus options B and C are correct
If Jacoby spins the spinner below 120 times, how many times can heexpect is to land on red?
Answer:
20 times
Explanation:
The spinner has 6 colors and 1 of them is red. So, the probability to land on red is
P = 1/6
Then, the expected number of times that the spinner will land on read can be calculated as the probability times 120, so
E = (1/6) x 120
E = 20
Therefore, the answer is 20 times
ate Fatuma Michele Simplify the expression below and identify the property used when eliminating the parentheses. 49 + 18 + 4 (29 + 9.5) 9+ The property was used to eliminate the parentheses. distributive commutative
Simplify the expression
[tex]\begin{gathered} 4q+18+4(2q+9.5)=4q+18+4\cdot2q+4\cdot9.5 \\ =4q+18+8q+38 \\ =12q+56 \end{gathered}[/tex]The distributive property is used to simplify the expression 4(2q + 9.5).
Answers:
12q + 56
Distributive property.
Please help:A magazine publisher’s profit as a function of subscribers is represented in the table. The function is quadratic.Subscribers (thousands)Monthly profit ($ thousands)000.75−11.251.50220390Select from the drop-down menu to correctly complete the sentence.The x-intercept represents The images of the answer choice are included
In a profit function the x-intercept always represent the breakeven point, that is, the point where the amount of money to produce the product or service is equal to the amount of money received.
Hence, in this case, the x-intercepts represents the number of subscribers when the publisher breaks even.