Determine the total cost for 3 order of fries and 2 drinks.
[tex]\begin{gathered} T=3\cdot0.94+2\cdot1.04 \\ =2.82+2.08 \\ =4.9 \end{gathered}[/tex]Determine the expression for f orders of fries and d drinks.
[tex]\begin{gathered} T=f\cdot0.94+d\cdot1.04 \\ =0.94f+1.04d \end{gathered}[/tex]So cost of 3 order of fries and 2 drinks is $4.9.
The cost order for f orders of fries and d drinks is 0.94f + 1.04d.
The figure shows the measures of various angles of a roof and it supports. Find the measure of angle 1, the angle between an eave and a horizontal support beam.
Answer:
35 degrees.
Explanation:
The figure shown is an isosceles triangle. An isosceles triangle has two of its sides and base angles to be equal.
Since the sum of the angles in a triangle is 180 degrees, hence:
110 + (base angles) = 180
110 + (<1 + <1) = 180 (since base angles are the same)
110 + 2<1 = 180
2<1 = 180-110
2<1 = 70
Divide both sides by 2
2<1/2 = 70/2
<1 = 35 degrees
Hence the angle between an eave and the horizontal support beam is 35 degrees.
72bz +96b2h + 90xbz + 120xbh +
Factoring
Factor the expression:
[tex]72b^2z+96b^2h+90xbz+120xbh[/tex]Divide the expression into two halves:
[tex](72b^2z+96b^2h)+(90xbz+120xbh)[/tex]Factor b^2 from the first group and xb from the second group:
[tex]b^2(72z+96h)+xb(90z+120h)[/tex]Now find the greatest common multiple of 72 and 96:
72= 2*2*2*3*3
96=2*2*2*2*2*2*3
Now we take the common factors with their least number of repetitions:
GCF=2*2*2*3=24
Now we find the GCF of 90 and 120:
90=2*3*3*5
120=2*2*2*3*5
GCF=2*3*5=30
Taking the GCF of each group:
[tex]\begin{gathered} b^224(3z+4h)+xb30(3z+4h) \\ =24b^2(3z+4h)+30xb(3z+4h) \end{gathered}[/tex]Now we finally take out 3z+4h from both groups:
[tex]\mleft(3z+4h\mright)(24b^2+30xb)[/tex]This last expression can be further factored by taking out 6b from both terms:
[tex]6b(3z+4h)(4b+5x)[/tex]This is the final expression factored as much as possible
How many solutions will each equation have?x^2+6x+5
To solve the quadratic equation, factor the expression and then clear x from each of the factors obtained.
[tex]\begin{gathered} x^2+6x+5=0 \\ (x+5)(x+1)=0 \\ x+5=0 \\ x=-5 \\ x+1=0 \\ x=-1 \end{gathered}[/tex]This equation has 2 solutions which are -5 and -1.
Expand the polynomial. 1. (m^2-n)(m^2+2n^2)2. (a-2)(4a^3-3a^2)
1)
The given polynomial is
[tex](m^2-n)(m^2+2n^2)[/tex]Multiply as follows:
[tex](m^2-n)(m^2+2n^2)=m^2(m^2+2n^2)-n(m^2+2n^2)[/tex][tex]=m^2\times m^2+m^2\times2n^2-n\times m^2-n\times2n^2[/tex][tex]=m^4+2m^2n^2-m^2n-2n^3[/tex]Hence the required expansion is
[tex](m^2-n)(m^2+2n^2)=m^4+2m^2n^2-m^2n-2n^3[/tex]2)
The given polynomial is
[tex](a-2)(4a^3-3a^2)[/tex]Multiply as follows:
[tex](a-2)(4a^3-3a^2)=a(4a^3-3a^2)-2(4a^3-3a^2)[/tex][tex]=a\times4a^3-a\times3a^2-2\times4a^3-(-2)\times3a^2[/tex][tex]=4a^4-3a^3-8a^3+6a^2[/tex][tex]=4a^4-11a^3+6a^2[/tex]Hence the required expansion is
[tex](a-2)(4a^3-3a^2)=4a^4-11a^3+6a^2[/tex]Hello, I need some assistance with this precalculus question, please?HW Q8
STEP - BY - STEP EXPLANATION
What to find?
• The system of equation of the argumented matrix.
,• The resultant after the given row operations.
Given:
The system of equation is:
7x - 7y + z = -5
3x - 3y + 8z = -5
-6x + y + 3z = 7
Hence, the correct option is D
The following row operations are to be performed;
[tex]\begin{gathered} R_1=-2r_2+r_1 \\ \\ R_3=2r_2+r_3 \end{gathered}[/tex]The first row operation implies that you will multiply row 2 by -2 and then add to row. The resultant gives a new row 1.
This means that the elements in row 1 becomes:
Row 1 : 1 -1 - 15 | 5
Row 2: 3 -3 8 | -5
As for row 3, we will multiply row 2 by 2 and then add to row 3 to get a new row 3.
That is;
Row 3 : 0 -5 19 | -3
ANSWER
Option D
Part B
[tex]\begin{bmatrix}{1} & {-1} & {-15\text{\mid}} & {5} \\ {3} & {-3} & {8\text{ }}| & {-5} \\ 0{} & -5{} & {19\text{ }|} & {-3} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}}\end{bmatrix}[/tex]1 -1 - 15 | 5
3 -3 8 | -5
0 -5 19 | -3
Price of PensWhat is the slope ofthe line?Price ($)0-NW A o ovo2Give your answer asa fraction in simplestform.11 2 3 4 5 6 7 8 9Number of Pens
Solution
For this case we can select the following two points:
(0,0) and (4,6)
We can find the slope using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-0}{4-0}=\frac{3}{2}[/tex]then the answer after simplify would be:
3/2
AcuveDetermining If a Number Is a SolutionQUICK CHECKWhich values are solutions to the inequality -3x – 4< 2? Check all of the boxes that apply.-4-2OOO03DONE
We have the next inequality given:
[tex]-3x-4<2[/tex]Solve the x variable:
Add both sides 4
[tex]\begin{gathered} -3x-4+4<2+4 \\ -3x<6 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{-3}{3}x<\frac{6}{3} \\ -x<2 \end{gathered}[/tex]Finally, multiply both sides by -1:
[tex]\begin{gathered} (-1)(-x)<2(-1) \\ x>-2 \end{gathered}[/tex]Hence, x can take any value greater than -2.
So, the solutions that apply are 0 and 3.
Find the 100-th term of the following sequence
3, 10, 17, 24, …
Also find the sum of the first 100 terms.
Answer:
696
Step-by-step explanation:
*nth term = 7n - 4
n = 100
7 × 100 - 4 = 696
So the 100th term of the following sequence is: 696
*To find the nth term:
They all increase by 7 so it is 7n3 - 7 = -4 so then it is 7n - 4Answer:
Below in bold.
Step-by-step explanation:
This is an arithmetic sequence with a1 = 3 and d = 7.
So, 100th term
= a1 + d(n - 1)
= 3 + 7(100-1)
= 696.
Sum (100) =
(n/2)[2a1 + d(n - 1)]
= 50(6 + 99*7)
= 50 * 699
= 34950.
I'm not sure if you can exactly give me the answers, but I need help solving these types of questions, I will attach them below. they are about tangent lines.
Question 1
Explanation
To solve these types of questions, we will use the Tangent radius theorem
Tangent to a Circle Theorem
The tangent theorem states that a line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.
The figure below helps give a pictorial view
The principle to be used here for question 1 will be
[tex]x^2+8^2=17^2[/tex]Simplifying further
[tex]\begin{gathered} x^2+64=289 \\ x^2=289-64 \\ x^2=225 \\ x=\sqrt{225} \\ x=15 \end{gathered}[/tex]Thus, the value of x is 15 units
Solve graphically by the intersection method. Give the solution in interval notation.5x+2<2x−4
The green line represents 5x + 2
The purple line represents 2x - 4
The orange-colour line represents the intersection of the lines above, which is the solution to the inequality:
5x + 2 < 2x - 4
The intersection is represented by a broken line, to signify the strict < in the equation
5(3a-1) - 2(3a+2)=3(a+2) + vselect two expressions that are equivalent to v.
Let's solve the equation for v to identify the expressions:
[tex]\begin{gathered} 5(3a-1)-2(3a+2)=3(a+2)+v \\ 15a-5-6a-4=3a+6+v \\ 9a-9=3a+6+v \\ v=9a-3a-9-6 \\ v=6a-15 \\ v=3(2a-5) \end{gathered}[/tex]Therefore the equivalent expressions are D and E
select all of the following equations which represent a function?
To verify that something is a function, we use the horizontal line rule. That is, if the horizontal line passes through two points, then the graph is not a function, like this:
Then the circles and the ellipses are not functions. Then the functions in the problem would be:
1, 3 and 6.
The answer for the bottom question need a fast quick answer
Area of a circle is
[tex]A=\pi\cdot r^2[/tex][tex]\begin{gathered} d=2r \\ d=22 \\ r=\frac{22}{2} \\ r=11 \end{gathered}[/tex][tex]\begin{gathered} A=\pi(11)^2 \\ A=380.133ft^2 \end{gathered}[/tex]The area of the garder is 380.13 square footsIf a square foot cost $ 1.25
[tex]\begin{gathered} 1ft^2\to1.25\text{dollars} \\ 380.13ft^2\to x \\ x=\frac{380.13ft^2\cdot(1.25dollar)}{1ft^2} \\ x=475.16\text{dollar} \end{gathered}[/tex]To cover the garden they need to buy $475 in mulchFind the domain of the function. Write the domain in interval notation.
The domain of a function is the possible values of "t" that the given function can take.
Since the variable "t" is in the denominator, the denominator cannot be equal to zero because it would make the function undefined.
Hence, t - 4 must be greater than zero. For t - 4 to be greater than zero, the value of t must be greater than 4.
In addition, since the variable is inside the radical sign, then the function itself cannot be negative.
Hence, the domain of this function must be greater than 4. In interval notation, it is (4, ∞).
i need help solving this with the statements and reasons
Given that:
[tex]\bar{AB}\mleft\Vert \mright?\bar{DC}[/tex]To prove that:
[tex]\Delta ABE\cong\Delta\text{CDE}[/tex]We know that congruent parts of congruent triangles are congruent
[tex]\angle\text{AEB }\cong\angle CDE\text{ (vertically opposite angles)}[/tex]Given that E is the midpoint of AC, therefore,
[tex]\begin{gathered} EA=EC\text{ } \\ EB=ED \end{gathered}[/tex]By the SAS congruency theorem as illustrated above, it is sufficient to prove that the triangles are congruent
find the other binomial p squared -13 p +36 =(p-9)
To find the other factor of the polynomial
[tex]p^2-13p+36[/tex]We need to find two integers which multiplication gives 36 and addition is -13.
This integers would be -9 and -4, then we have
[tex]p^2-13p+36=p^2-9p-4p+36[/tex]now we factor the right term using common factors:
[tex]\begin{gathered} p^2-9p-4p+36=p(p-9)-4(p-9) \\ =(p-9)(p-4) \end{gathered}[/tex]Hence:
[tex]p^2-9p-4p=(p-9)(p-4)[/tex]Therefore, the other binomial we are looking for is (p-4).
hey i need help giving 10 points
Answer:
B(2) = -1
Step-by-step explanation:
Assuming each division on the grid is 1 unit
Locate 2 on the x-axis. That is two divisions to the right of the origin. The y value corresponding to this is -1
Which of the following are equal to sec x? Choose all that apply. 3 answers
Verify each option
A ---> 1/sinx=cscx -----> is not the answer
B ---> 1/cosx=secx ----> is the answerC ---> cosx/tanx=cosx/(sinx/cosx)=cos^2x/sinx -----> is not the answer
D ---> tanx/sinx=(sinx/cosx)/sinx=1/cosx=secx -----> is the answerE ---> cotxsinx=(cos/sinx)sinx=cosx ----> is not the answer
F ----> tanxcscx=(sinx/cosx)(1/sinx)=1/cosx=secx ----> is the answertherefore
The answer is
options B, D and FAnswer:
B, D, E.
Step-by-step explanation:
B: [tex]\frac{1}{cos(x)}[/tex]
D: [tex]\frac{tan(x)}{sin(x)}[/tex]
E: [tex]tan(x) csc (x)[/tex]
Jordan plotted the graph below to show the relationship between the temperature of his city and the number of cups of hot chocolate he sold daily:A scatter plot is shown with the title Jordans Hot Chocolate Sales. The x axis is labeled High Temperature and the y axis is labeled Cups of Hot Chocolate Sold. Data points are located at 20 and 20, 30 and 18, 40 and 20, 35 and 15, 50 and 20, 45 and 20, 60 and 14, 65 and 18, 80 and 10, 70 and 8, 40 and 2.Part A: In your own words, describe the relationship between the temperature of the city and the number of cups of hot chocolate sold. (2 points)Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept. (3 points)
A.
Overall it has a relation that there are more sold cups when the temperature is lower. On the other hand, based on the 40 degrees part, that have to different values of two different days, we can say is not the only factor.
B.
The best lineal approach is the line created with the points at 20 and 80 degrees. First the slope:
[tex]m=\frac{y1-y2}{x1-x2}=\frac{20-10}{20-80}=\frac{10}{-60}=-\frac{1}{6}[/tex]Now the intercept with y axis, b:
[tex]\begin{gathered} y=mx+b \\ 20=20(-\frac{1}{6})+b \\ 20+\frac{20}{6}=b=23.33=\frac{70}{3} \end{gathered}[/tex]The final line formula is:
[tex]y=-\frac{x}{6}+\frac{70}{3}[/tex]Given a regular octagon and a regular nonagon, which one has the greater interior angle?(Type your answer as the name of the polygon)
Answer:
Nonagon
Explanation:
Each of the interior angles of a polygon is calculated using the formula:
[tex]\frac{180^0\mleft(n-2\mright)}{n}[/tex]An Octagon has 8 sides, therefore:
[tex]\begin{gathered} Each\; \text{Interior Angle=}\frac{180^0(8-2)}{\square} \\ =\frac{180\times6}{8} \\ =\frac{1080^0}{8} \\ =135^0 \end{gathered}[/tex]A Nonagon has 9 sides, therefore:
[tex]\begin{gathered} Each\; I\text{nterior Angle=}\frac{180^0(9-2)}{9} \\ =\frac{180\times7}{9} \\ =\frac{1260^0}{9} \\ =140^0 \end{gathered}[/tex]Therefore, the nonagon has a greater interior angle.
Find the x-intercepts and y-intercept of the following
function.
f(x) = (x+7) (x + 1)(x − 2)
Write your answer in coordinate pairs of the form (x, y).
Provide your answer below:
x-intercept: ().(
]).() and
y-intercept:
Step-by-step explanation:
there are 3 x-intercepts (the x- values when y = 0). because y is only 0, when one of the 3 factors is 0.
and that is the case for
x = -7
x = -1
x = 2
so, formally, the x- intercepts are
(-7, 0), (-1, 0), (2, 0)
the y intercept is the y- value when x = 0.
(0 + 7)(0 + 1)(0 - 2) = 7×1×-2 = -14
the y-intercept is formally
(0, -14)
74. Noam wants to put a fence around his rectangular garden. His garden measures 35 feet by 50 feet. Thegarden has a path around it that is 3 feet wide. How much fencing material does Noam need to enclose thegarden and path?A. 97 ftB. 194 ftC. 182 ftD. 146 ft
Given:
The length of the rectangular garden, l=50 feet.
The breadth of the rectangular garden, b=35 feet.
The width of the path around the garden, w=3 feet.
The figure can be drawn as,
So, the length of the fence, L=l+2w.
The breadth of the fence, B=b+2w
The perimeter of the fence can be calculated as,
[tex]\begin{gathered} P=2(L+B) \\ =2(l+2w+b+2w) \\ =2(l+b+4w) \\ =2(50+35+4\times3) \\ =2(50+35+12) \\ =2\times97 \\ =194\text{ ft} \end{gathered}[/tex]Therefore, the perimeter of the fence is 194 ft.
Option B is correct.
Ms. Mistovich and Ms. Nelson are having a competition to see who can get morestudents to bring in extra tissues for their classroom. Ms. Mistovich starts with 4 boxesand each week she gets two more boxes from her students. Ms. Nelson starts with 1box and each week she gets 3 more boxes from her students. Write a system ofequations to represent the situation. (1 pt)y=2x+4y=3x+1Ooy=2x+4y=2x+3y=4x+2y=3x+1y=2x+3y=4x+1o
To write an equation, it is enough to know the rate of change (slope) and the initial value (y-intercept).
The equation of a line of slope m and y-intercept b is:
[tex]y=mx+b[/tex]For Ms. Mistovich, the initial value is 4 and the rate of change is 2.
For Ms. Nelson, the initial value is 1 and the rate of change is 3.
Therefore, the equations that model this situation, are:
[tex]\begin{gathered} y=2x+4 \\ y=3x+1 \end{gathered}[/tex]How many tiles of 8 cm² is needed to cover a floor of dimension 6 cm by 24 cm? A. 6 B. 12 C. 18 D. 24
Answer:
18 tiles.
Step-by-step explanation:
24x6= 144
144/8= 18
vote for brainliest and have a nice day
At a school on Monday, 3 out of every 4 students were wearing shirts. There were 600 students present in school on Monday. How many of the students were wearing shirts? A. 599, because 600 - (4 - 3) = 599 B. 450, because C. 50, because 600 - (4 x 3) = 50 600 - Student D. 800, because 450 4= Students 3=sludents 4 600 600 800 so
3 out of 4 students mean
3/4th students were wearing shirts.
Total students = 600
So,
3/4th of 600 students were wearing shirt.
Let us calcualte (3/4)th of 600:
[tex]\begin{gathered} \frac{3}{4}\times600 \\ =\frac{3\times600}{4} \\ =\frac{1800}{4} \\ =450 \end{gathered}[/tex]Answer450 students
estimate 794 divided by 18=?
Answer:
C 40
Step-by-step explanation:
794 is about 800
18 is about 20
800/20=40
-Given that f(x) = 6(x - 1). Choose the correct statement. A. f-1(12) = 3.5 B. f-1(3) = 1 c. f-16) = 3 D. f-1(9) = 2.5
Given that function is f(x) = 6(x - 1).
Let y = 6(x - 1). Replace x with y and then solve for y.
[tex]\begin{gathered} x=6(y-1) \\ \Rightarrow x=6y-6 \\ \Rightarrow6y=x+6 \\ \Rightarrow y=\frac{x+6}{6} \end{gathered}[/tex]Thus, f^-1(x) = (x + 6)/6.
[tex]f^{-1}(12)=\frac{12+6}{6}=3[/tex][tex]f^{-1}(3)=\frac{3+6}{6}=1.5[/tex][tex]f^{-1}(6)=\frac{6+6}{6}=2[/tex][tex]f^{-1}(9)=\frac{9+6}{6}=2.5[/tex]Thus, option D is correct.
STATEMENTREASON1. DBC - RST1. Given2. ZABC - ZDBC+ ABD2. Angle addition therom3.3. Ifa=b+cand c>0,thena > b4. ABC > RST4. SubstitutionWhich of the following statements would complete the proof in line 3?O ZABC> ZABDO LABC> DBCO ZDBC> ZABD
Answer
Option B is correct.
Angle ABC > Angle DBC
Explanation
Since it's been proven that
Angle ABC = Angle ABD + Angle DBC
Since Angle ABD > 0,
Angle ABC > Angle DBC is the part that completes the proof that
Angle ABC > Angle RST
Hope this Helps!!!
Which point is part of the solution of the inequality y ≤ |x+2|-3A.(-1,-1)B.(1,0)C.(0,0)D.(0,1)
We are going to test all options to see which is true and false.
The one that is true will be the point that is part of the solution.
[tex]\begin{gathered} A) \\ (-1,-1) \\ y\leq\lvert x+2\rvert-3 \\ -1\leq\lvert-1+2\rvert-3 \\ -1\leq\lvert1\rvert-3 \\ -1\leq1-3 \\ -1\leq-2 \\ \text{Not true, so the point (-1,-1) is not a part of the solution} \end{gathered}[/tex]We will move to the next option and test:
[tex]\begin{gathered} B) \\ (1,0) \\ y\leq\lvert x+2\rvert-3 \\ 0\leq\lvert1+2\rvert-3 \\ 0\leq\lvert3\rvert-3 \\ 0\leq3-3 \\ 0\leq0 \\ \text{The above solution is true, so it is a point that is part of the solution.} \\ \text{The correct answer is option B.} \end{gathered}[/tex]Hi, can you help me answer this question please, thank you!
The sample size given in the question is
[tex]n=37[/tex]The mean weight is
[tex]\bar{x}=50[/tex]The standard deviation is
[tex]\sigma=8.4[/tex]The margin of error is calculated using the formula below
[tex]\text{MOE = Z-score(90\% C.I)}\times\frac{\sigma}{\sqrt[]{n}}[/tex]Using the Z-score table, the Z-score for the 90% confidence interval is
[tex]=1.645[/tex]By substituting the values in the formula above, we will have
[tex]\begin{gathered} \text{MOE = Z-score(90\% C.I)}\times\frac{\sigma}{\sqrt[]{n}} \\ \text{Margin of error(MOE)} \\ =1.645\times\frac{8.4}{\sqrt[]{37}} \\ =\frac{13.818}{\sqrt[]{37}} \\ =\pm2.272\text{ounces} \end{gathered}[/tex]Hence,
The final answer is = ±2.272 ounces
