Given the vector represented by:
[tex]8a[/tex]You know that:
[tex]a\langle-4,2\rangle[/tex]By definition, the Component Form of a vector is:
[tex]\vec{V}=\langle x,y\rangle[/tex]In this case, you only need to multiply the coordinates of "a" by 8, in order to find the Component Form of:
[tex]8a[/tex]Therefore, you get:
[tex]=\langle(8)(-4),(8)(2)\rangle=\langle-32,16\rangle[/tex]Hence, the answer is:
[tex]\langle-32,16\rangle[/tex]Determine whether the relation is a function.13) {(-6, -5), (-3, -7), (4, 6), (4,8)}A) Not a functionB) Function
A) Not a function
ExplanationA function is a relation which describes that there should be only one output for each input
Step 1
let's check the given ordered pair
[tex]\begin{gathered} (x,y),\text{ x is the input, y is the output} \\ (-6,5)\text{ , -6}\Rightarrow5 \\ (-3,-7),\text{ -3}\Rightarrow-7 \\ (4,6),\text{ 4}\Rightarrow6 \\ (4,8).\text{ 4}\Rightarrow8 \end{gathered}[/tex]we can see that
the input 4 has 2 outputs 6 and 8, so
this is not a function, hence the answer is
A) Not a function
I hope this helps you
the base of the pyramid is a square. the volume is ___ cubic cm. measurements:l = 6 cmw = 10 h = 15(unable to send pictures of question without app crashing. my apologies.)
Answer:
300 cubic meters.
Explanation:
The volume of any pyramid is obtained using the formula below:
[tex]V=\frac{1}{3}\times\text{Base Area}\times Height[/tex]Substitute the given values:
[tex]\begin{gathered} V=\frac{1}{3}\times(6\times10)\times15 \\ =\frac{1}{3}\times60\times15 \\ =300\operatorname{cm}^3 \end{gathered}[/tex]The volume of the pyramid is 300 cubic meters.
Question 1-6
Miriam is buying popsicles for her soccer team. She wants to spend the same amount of money at two different businesses. Food Hub sells popsicles for $1.75 each with a delivery fee of
$5.00 and Foodie Eats sells popsicles for $1.80 each with a delivery fee of $4.39. She wrote an equation to determine the number of popsicles, p, she can buy. Her work is shown below.
1.75p+5 = 1.80p + 4.39
-1.75p
-1.75p
5 = 0.05p + 4.39
- 4.39
-4.39
0.61 0.05
0.05 0.05
12.2 = p
Is the solution to this equation viable in this context?
The solution
viable because she
From the given data , the required equation to find the number of popsicles 'p' which Miriam can buy is given by 1.75p +5 = 1.80p + 4.39 is equal to p =12 .
Solution is viable as we can take the nearest round off value to find the number of popsicles.
As given in the question,
Two different companies where Miriam want to spend same amount of her money.
Equation of Food Hub sells is:
1.75p + $5.00
Equation of Foodie eat sells:
1.80p + $4.39
Where p is the number of popsicles
Required relation to get the value of p we have,
1.75p + 5.00 = 1.80p + 4.39
Take like terms on same side we get,
1.80p - 1.75p = 5.00 -4.39
⇒ 0.05p = 0.61
⇒ p = 12.2
⇒ p = 12 (round off number)
Number of popsicles cannot be in decimals.
Solution is viable as we can take the nearest round off value to find the number of popsicles.
Therefore, from the required equation to find the number of popsicles 'p' which Miriam can buy is given by 1.75p +5 = 1.80p + 4.39 is equal to p =12
Solution is viable as we can take the nearest round off value to find the number of popsicles.
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The fox population in a certain region has a continuous growth rate of 9 percent per year.
SOLUTION
The function can be derived from the model
[tex]\begin{gathered} P=P_oe^{(\ln r)t^{}} \\ \\ r\text{ here represents 1 + 9 percent growth rate } \end{gathered}[/tex]So the function becomes
[tex]P(t)=2000_{}e^{(\ln 1.09)t}[/tex]So the fox population in 2008
2008 - 2000 = 8
So our t becomes 8
The population becomes
[tex]\begin{gathered} P=2000_{}e^{(\ln 1.09)t} \\ P=2000_{}e^{(\ln 1.09)\times8} \\ P=\text{ }2000_{}e^{0.086177\times8} \\ =2000_{}e^{0.6894} \\ =\text{ 3985.04} \end{gathered}[/tex]So the Population = 3985
find the measures of the angles labeled in the figure below. measure of angle EFD=measure of angle EHF=measure of angle HFG=measure of angle G=
EXPLANATION:
We must bear in mind that the internal angles of a triangle must add up to 180 degrees.
We will first find values of unknown angles and finally add to find the corresponding measures.
[tex]\begin{gathered} To\text{ find F:} \\ corresponds\text{ }to\text{ the same angle }measure\text{ }54(F) \\ To\text{ find G:} \\ We\text{ add }the\text{ two internal }angles\text{ 54 }and\text{ s}ubtract\text{ }180\colon \\ 54+54=180 \\ 180-54-54 \\ 180-108 \\ 72\text{ ( }angle\text{ G)} \\ To\text{ find E;} \\ We\text{ must }the\text{ measures }H\text{ and G} \\ H=54\text{ ; G= 72 E=X} \\ 54+72=180 \\ 180-54-72 \\ 54(\text{Angle E)} \\ To\text{ find D} \\ We\text{ must the measures: 33 +54 and }substract\text{ 180} \\ 33+54=180 \\ 180-33-54 \\ 93\text{ (angle D)} \end{gathered}[/tex]Now to find the measurements given in the exercise; We must take the values found according to what each exercise asks for and add them.
[tex]\begin{gathered} \text{Measure of angle EFD:} \\ E(54)+\text{ F(54})+D(93)=201 \\ \text{Measure of angle EHF:} \\ E(54)+H(54)+F(54)=162 \\ \text{Measure of angle HFG:} \\ H(54)+F(54)+G(72)=180 \\ \text{Measure of angle G:} \\ G=\text{ 72 degr}ees \end{gathered}[/tex]use the function f(x)=-3(x+1)2+18what is the y intercept ?does it have a max or min
hello,
First of all, we must remember that a first degree function must be in the formula f (x) = ax + b, so, lets use this form:
[tex]undefined[/tex]Find the length of each side of an equilateral triangle with perimeter 36 inches.Provide your answer below:inches4
1) Given that an equilateral triangle has three congruent sides, so we can tell that each side has the following measurement:
[tex]\begin{gathered} P_{\Delta}=l+l+l\Rightarrow P_{\Delta}=3l \\ 3l=36 \\ \frac{3l}{3}=\frac{36}{3} \\ l=12" \end{gathered}[/tex]Note that since they are congruent then we can tell that.
Make the following conversion in the metric system by multiplying by the appropriate conversion factor. Write your answer as a whole number or decimal.20 m to millimeters ?mm
Each meter has 100 centimeters, each centimeters has 10 milimeters, so 20 meters has 20.000 milimeters.
Hello. I need help with this practice problem. I will include a picture. Thank you soo much
Firstly, we need to compare the information ew have from both sides of the equation, the denominators.
The different between the denominator is that the right side has the factor (w + 6), while the lest side does not.
So, sstarting from the expression on the left side, we can introduce the factor (w + 6) into the denominator by multiplying both the numerator and the denominator by this factor:
[tex]\frac{2}{w+7}=\frac{2}{w+7}\cdot\frac{w+6}{w+6}=\frac{2(w+6)}{(w+7)(w+6)}[/tex]The order of the factor dont change the result, so we can switch the factors on the denominator to get:
[tex]\frac{2}{w+7}=\frac{2(w+6)}{(w+6)(w+7)}[/tex]Now, by comparison, we can see that the blank part is the following:
[tex]2(w+6)[/tex]Samson buys a newcomputer for class. Thecomputer costs $550, aswell as an additional tax of10.2%.How much does he pay forthe computer?
The cost of the computer is: $550
The additional tax is: 10.2%
To find the final cost of the computer, first, we need to find how much is the tax of 10.2%.
Step 1. Calculate how much is 10.2% of $550.
In general, to calculate a percentage we divide the quantity by 100 and then multiply by the percentage we need. In this case:
[tex]\frac{550}{100}\times10.2[/tex]Solving the operations:
[tex]5.5\times10.2[/tex][tex]=56.1[/tex]The tax is $56.1
Step 2. Add the cost of the computer and the tax to find how much he paid for the computer:
[tex]550+56.1=606.1[/tex]Answer: $606.1
Micha starts riding his bike at 12:05pm Her rides for 35 minutes What time does he stop riding his bike?
If Micha rides for 35 minutes, she'll stop riding her bike at 12:40pm
Solve VABC if a = 34 feet, b = 20 feet, and c = 18 feet. .
Cosine theorem:
[tex]\begin{gathered} a^2=b^2+c^2-2bccosA \\ b^2=a^2+c^2-2ac\cos B \\ c^2=a^2+b^2-2ab\cos C \end{gathered}[/tex]a= 34ft
b = 20ft
c = 18ft
[tex]\begin{gathered} a^2-b^2-c^2=-2bc\cos A \\ \frac{a^2-b^2-c^2}{-2bc}=\cos A \\ \\ A=\cos ^{-1}(\frac{a^2-b^2-c^2}{-2bc}) \end{gathered}[/tex][tex]B=\cos ^{-1}(\frac{b^2-a^2-c^2}{-2ac})[/tex][tex]C=\cos ^{-1}(\frac{c^2-a^2-b^2}{-2ab})[/tex][tex]\begin{gathered} A=\cos ^{-1}(\frac{34^2-20^2-18^2}{-2(20)(18)}) \\ \\ A=\cos ^{-1}(\frac{432}{-720})=126.86 \end{gathered}[/tex][tex]\begin{gathered} B=\cos ^{-1}(\frac{20^2-34^2-18^2}{-2(34)(18)}) \\ \\ B=\cos ^{-1}(\frac{-1080}{-1224})=28.07 \end{gathered}[/tex][tex]\begin{gathered} C=\cos ^{-1}(\frac{18^2-34^2-20^2}{-2(34)(20)}) \\ \\ C=\cos ^{-1}(\frac{-1235}{-1360})=24.75 \end{gathered}[/tex]VABC:
A=126.86º
B=27.07º
C=24.75º
a=34ft
b=20ft
c=18ft
751 body temperature measurements were taken. The sample data resulted in a sample mean of 98.1 F and a sample standard deviation of 0.7 F. Use the traditional method and a 0.05 significance level to test the claim that the mean body temperature is less than 98.6 F.
The mean value of the sample is 98.1 F and its standard deviation is 0.7 F.
The margin of error of the mean value is given by 0.7/sqrt(751) = 0.7/27.4 = 0.026 (rounded to the nearest thousandth)
Using the Z test, we got: Z = (98.6 - 98.1)/(0.026) = 0.5/0.026 = 196
Therefore, the mean value of the sample is incompatible with 98.6 and we can claim that the mean body temperature is less than it.
How to graph inequalities y + 6 < 10 or 2y - 3 > 9
We need to graph on the number line the solution to the compounded inequality
[tex]\begin{gathered} y+6<10 \\ \text{or } \\ 2y-3>9 \end{gathered}[/tex]In order to do so, let's work with each inequality separately. The final solution will be the union of the two solutions since it can be one "or" the other.
Step 1
Subtract 6 from both sides of the first inequality:
[tex]\begin{gathered} y+6<10 \\ \\ y+6-6<10-6 \\ \\ y<4 \end{gathered}[/tex]So, the solution to the first inequality is all real numbers less than 4 (not included). Therefore, we graph this solution using an empty circle:
Step 2
Add 3 to both sides of the second inequality, and then divide both sides by 2:
[tex]\begin{gathered} 2y-3+3>9+3 \\ \\ 2y>12 \\ \\ \frac{2y}{2}>\frac{12}{2} \\ \\ y>6 \end{gathered}[/tex]Thus, the solution to this inequality is all the real numbers greater than 6 (not included: empty circle):
Answer
Therefore, the solution to the compounded inequalities is the union of both solutions:
NEED HELP DUE BY WEDNESDAY OR TOMMOROW. Solve each of the equations and select the numbers that represent solutions to more than one of the six equations. Select all that apply. 4x-3=17 8(x + 1) = 24 5(x - 2) = 20 34 - 7x = 20 31 - x = 29 3x +6=21. A. x=1. B. x=2. C. x=3. D. x=4.E. x=5. F. X = 6.
Given
The equations,
4x-3=17, 8(x + 1) = 24, 5(x - 2) = 20, 34 - 7x = 20, 31 - x = 29, 3x +6=21.
To find the solution to each equations.
Explanation:
It is given that,
The equations,
4x-3=17, 8(x + 1) = 24, 5(x - 2) = 20, 34 - 7x = 20, 31 - x = 29, 3x +6=21.
That implies,
1)
[tex]\begin{gathered} 4x-3=17 \\ 4x=17+3 \\ 4x=20 \\ x=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Hence, the solution is x=5.
2)
[tex]\begin{gathered} 8(x+1)=24 \\ x+1=\frac{24}{8} \\ x+1=3 \\ x=3-1 \\ x=2 \end{gathered}[/tex]Hence, the solution is x=2.
3)
[tex]\begin{gathered} 5(x-2)=20 \\ x-2=\frac{20}{5} \\ x-2=4 \\ x=4+2 \\ x=6 \end{gathered}[/tex]Hence, the solution is x=6.
4)
[tex]\begin{gathered} 34-7x=20 \\ 34-20=7x \\ 7x=14 \\ x=\frac{14}{7} \\ x=2 \end{gathered}[/tex]Hence, the solution is x=2.
5)
[tex]\begin{gathered} 31-x=29 \\ 31-29=x \\ x=2 \end{gathered}[/tex]Hence, the solution is x=2.
6)
[tex]\begin{gathered} 3x+6=21 \\ 3x=21-6 \\ 3x=15 \\ x=\frac{15}{3} \\ x=5 \end{gathered}[/tex]Hence, the solution is x=5.
May you help me with this
Given the function
[tex]h(x)=2x^2-3x+5[/tex]Set x=-3 and solve for h(-3) as shown below
[tex]\begin{gathered} x=-3 \\ \Rightarrow h(-3)=2(-3)^2-3(-3)+5=18+9+5=32 \\ \Rightarrow h(-3)=32 \end{gathered}[/tex]Therefore, the answer is 32
Connie is studying two number patterns. Pattern 1 starts at 0 and has the rule "add 4.Pattern 2 starts at 0 and has the rule "add 2."Drag a number into each box to complete Connie's patternsDrag a phrase into the last box to complete the comparison of the corresponding terms in each pattinPattern 1:0,
Let's start with Pattern 1.
SInce the rule is to add 4, we shall add 4 on the first number that is zero.
The pattern 1 shall be:
[tex]0,4,8,12[/tex]On the other hand, for Pattern 2, the rule is to add 2. So, let's add 2 on the first number that is 0. Pattern 2 shall be:
[tex]0,2,4,6[/tex]Based on these two patterns, we can see that the terms in Pattern 1 are two times the corresponding terms in Pattern 2.
Using the diagram below, select all angles that are congruent.DLEoThere are three answers.O ZDOCО / ВОСO ZAOCZAOBZDOBEODDEOCO
We don't know the actual measures of the angles in the diagram but three of them have the same mark. This indicates that the angles are equal.
So the angles ∠EOD, ∠BOC and ∠AOB can be considered congruent.
I have a practice problem that I need explained an answered, thank you
From the question, we are given the matrices
We are to find which operation is defined and whic one is not
For the operation
[tex]M-N[/tex]For subtraction operation to be definded
The order of the matrices must be the same
Since the order of M is 4 x 2
And the order of N is 4 x 2
Therefore, the operation M - N is defined
For the operation
[tex]L-N[/tex]Similarly, for the operation to be definded
The order of the matrices must be the same
The oder of matrix L is 2 x 2 while the order of matrix N is 4 x 2
Since the oder of the matrices are not the same then
The operation L - N is not defined
For the operation
[tex]M+P[/tex]For addition operation to be defined, the Order of the matrices must be the same
The order of matrix M is 4 x 2 while the order of matrix P is 2 x 2
Since the order of the matrices are not the same then the operation is not defined
For the operation
[tex]Q+P[/tex]For addition operation to be defined, the Order of the matrices must be the same
The order of matrix Q is 2 x 1 while the order of matrix P is 2 x 2
Since the order of the matrices are not the same then the operation is not defined
Keisha has four favorite shirts one blue, one green, one red, one yellow and two favorite pairs of pants one black and one brown she decides to randomly choose a pair of pants and a shirt to wear for the day. What is the probability that Keisha chooses and outfit that is yellow and black or red and brown round your answer to the nearest whole percent?
Answer:
25%
Explanation:
First, let's calculated the total number of outfits that Keisha can choose. So, we will use the rule of multiplication as:
4 * 2 = 8
Shirts Pants
Because she has 4 options for shirts and 2 options for pants. So, there 8 possible outfits.
Then, from those outfits, there is 1 that is yellow and black, and 1 that is red and brown. So, the probability that Keisha chooses an outfit that is yellow and black or red and brown is:
[tex]P=\frac{1+1}{8}=\frac{2}{8}=0.25=25\text{ \%}[/tex]Therefore, the answer is 25%
an office administrator has an office supply budget $150. The office administrator will purchase folders, which are $2.15 each and notebooks, which are $4.60 each. which inequality represent the constrain on the number of folders f and notebook n the office administrator can purchase
If the price of each folder is $2.15, and the amount of folders is f, the total price paid for folders is the product of the unitary price by the amount bought.
[tex]\text{price}1=2.15f[/tex]Similarly, the price paid for notebooks is the unitary price of one notebook ($4.60) multiplied by the amount of notebooks (n).
[tex]\text{price}2=4.6n[/tex]Finally, the total cost of both products together is the sum of these products.
[tex]\text{cost}=\text{price}1+\text{price}2=2.15f+4.6n[/tex]The supply budget is $150, so the total cost needs to be lesser than or equal this value.
Therefore, we have that:
[tex]\begin{gathered} \text{cost}\le150 \\ 2.15f+4.6n\le150 \end{gathered}[/tex]So the correct option is B.
Need help confirming my answer, do I just put x=1 or x=1,-3/2
Applying quadratic formula to the given quadratic equation, we get the solutions as [tex]x=1,-\frac{3}{2}[/tex].
It is given to us that the quadratic equation is -
[tex]-2x^{2} -1x+3=0[/tex] ---- (1)
We have to solve by this by quadratic formula.
From equation (1), we have
[tex]-2x^{2} -1x+3=0\\= > -2x^{2} -x+3=0\\= > -(2x^{2} +x-3)=0\\= > 2x^{2} +x-3=0[/tex]----- (2)
The above equation (2) is in the form of a quadratic equation
[tex]ax^{2} +bx+c=0[/tex]
where, a = 2
b = 1
and, c = -3
Now, using the quadratic formula, we know
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] and, [tex]x=\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]
Substituting the values of a, b, and c in the above formulas to find the value of x, we get
[tex]x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} and x=\frac{-b-\sqrt{b^{2} -4ac} }{2a}\\= > x=\frac{-1+\sqrt{(-1)^{2} -4*2*(-3)} }{2*2} and x=\frac{-1-\sqrt{(-1)^{2} -4*2*3} }{2*2}\\= > x=\frac{-1+\sqrt{25} }{4} and x=\frac{-1-\sqrt{25} }{4}\\= > x= \frac{-1+5}{4} and x=\frac{-1-5}{4} \\= > x=\frac{4}{4} and x=\frac{-6}{4} \\= > x=1 and x= -\frac{3}{2}[/tex]
Thus, solving the given quadratic equation through quadratic formula, we get the solutions as [tex]x=1,-\frac{3}{2}[/tex].
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taliyah 1. If Mrs. Wozniak runs 8 miles a day. How many miles will she run in 4 weeks? Your answer 2. Fach fourth trade class at a local elementan answered 1 209 multiplication fact problems last
Use the given rate to find how many miles will Mrs. Wozniak run in 4 weeks. Remember that 1 week is equal to 7 days, then 4 weeks is 28 days.
[tex]28days\cdot\frac{8miles}{1day}=224miles[/tex]She will run 224 miles in 4 weeks.
In ABC, A = 68°, a = 14 and c = 17. Which of these statements best describes the triangle?
Given for the triangle ABC:
[tex]\begin{gathered} \angle A=68\degree \\ a=14,c=17 \end{gathered}[/tex]Using the sine rule, we will solve the triangle by finding the missing angles
So,
[tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex]substitute with the given data:
[tex]\begin{gathered} \frac{14}{\sin68}=\frac{17}{\sin C} \\ \\ \sin C=\frac{17}{14}\cdot\sin 68=1.125866 \end{gathered}[/tex]The value of (sin C) must be 1 or less than 1
So, the triangle ABC cannot be constructed
The answer will be the last option
Let f(x)=3x - 4. Write a function gwhose graph is a reflection of the graphoff.
hello
the function given is
5 points10) Some sixth-, seventh-, and eighth-grade students spend time at theelementary school tutoring students. Of the students who tutor, 12 aresixth-graders, 18 are seventh-graders, and 6 are eighth-graders. Whatpercent of tutors are seventh-graders? *18%36%50%75%
50%
1) Gathering the data
12 are 6th graders
18 7th graders
6 8th graders
2) Let's add them up at first to get the whole number of students who tutor:
12 +18 +6 = 24 +12 = 36
So we can say that
36 -------------- 100%
The 7th graders: 18 students
So we can write a proportion for that
36-------100%
18 ------- x
36x = 1800 Divide both sides by 36
x =50
3) So the answer is 50% of them are 7th graders.
is 13/4 and 21/4 equivalent an equivalent fraction?
To determine if they are equivalent we equal them and if when simplified they do not show the same values, they are not. That is:
[tex]\frac{13}{4}=\frac{21}{4}\Rightarrow3.25\ne5.25[/tex]From that, we can see that they are not equivalent fractions.
1 11a.) A sign in a bakery gives the following options. Find each unit price to the nearest cent, and show your reasoning. You can get 3 mini-cakes for $32. What is the cost of ONE mini-cake? * O $10.66 O $10.65 O $10.67 O $10.59
Since we can get 3 mini-cakes for $32, we can find the price of each mini-cake by taking the ratio of price to number of mini-cakes, like this:
unit price = 32/3 = 10.67
Then, the cost of ONE mini-cake is $10.67
Arthur has 20/8 cups of dishwashing detergent. He uses 1/4 cup of detergent for each load of dishes. what is the greatest number of loads of dishes Arthur was with this amount of detergent
Total = 20/8 cups of dishwashing detergent.
he has 20/8 = 5/2 = 2 1/2 cups of dishwashing detergent, per load he uses 1/4
per load
2 1/2 - 1/4
_____________________
The general formula
x= number of loads
20/8 - x* 1/4= 0
20/ 8 = x 1/4
x 1/4 = 20/ 8
x= 4* (20/8 )
x= 10
The greatest number of loads of dishes Arthur was with this amount of detergent is 10
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The number of compounding periods is equal to what: what is the formuls
Answer
When compound interest is discussed, the time rate for the compound interest is usually mentioned. For example, they would say that
- a certain amount of money has its interest compounded at 5% annually,
- a certain amount of money has its interest compounded at 7% every 3 months,
- a certain amount of money has its interest compounded at 2% every 6 months,
In each of the examples given above, the compounding period is 1 year, 3 months and 6 months respectively.
If one is now asked to calculate the compound interst on a particular amount of money after time, T, we usually express this time T in terms of the number of time periods, t, that exist inside the given time T.
Hence, the time T is expressed in terms of time period t, as
T = nt
Such that the number of compounding periods in T is given as
n = (T/t)
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