Answer:13
Step-by-step explanation:
Step-by-step explanation:
remember, when 2 signs and/operations come together, for addition/subtraction and multiplication/division it always applies :
+ + = +
- + = -
+ - = -
- - = +
and therefore,
9 - (-4) = 9 + 4 = 13
a minus meeting a minus always results in a plus.
What is the output value for the following function if the input value is 5?y = 4x - 34223172
Answer:
17
Explanation:
Given the function:
[tex]y=4x-3[/tex]When the input value, x = 5
[tex]\begin{gathered} y=4x-3 \\ =4(5)-3 \\ =20-3 \\ =17 \end{gathered}[/tex]The output value if the input value is 5 is 17.
Find a unit vector u with the same direction as v = : (-3, 8)
Given:
The vector
[tex]v=<-3,8>[/tex]Required:
To find the unit vector u with the same direction.
Explanation:
Unit formula is the vector is divided by its magnitude.
Now the magnitude of v is,
[tex]\begin{gathered} mag.v=\sqrt{(-3)^2+8^2} \\ =\sqrt{9+64} \\ =\sqrt{73} \end{gathered}[/tex]Now the unit vector is,
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]Final Answer:
[tex]u=<-\frac{3}{\sqrt{73}},\frac{8}{\sqrt{73}}>[/tex]Suppose that you follow the same path on the return trip from Dubuque to Council Bluffs. What would be thetotal number of (actual) miles for the round trip?
We know the trip from Council Bluffs to Dubuque had a total distance of 348 miles; if we take the same route to go back this will mean that we need to travel the same distance, 348 miles. The total distance then we will be 696 miles.
What are the possible values for the missing term of the geometric sequence? .004, _____, .4.04.04, -.04.0004.0004, -.0004
By definition, in a Geometric sequence the terms are found by multiplying the previous one by a constant. This constant is called "Common ratio".
In this case, you know these values of the set:
[tex]\begin{gathered} .004 \\ .4 \end{gathered}[/tex]Notice that you can set up this set with the value given in the first option:
[tex].004,.04,.4[/tex]Now you can check it there is a Common ratio:
[tex]\begin{gathered} \frac{0.04}{0.004}=10 \\ \\ \frac{.4}{0.04}=10 \end{gathered}[/tex]The Common ratio is:
[tex]r=10[/tex]Therefore, it is a Geometric sequence.
Apply the same procedure with each option given in the exercise:
- Using
[tex].004,.04,-.04,.4[/tex]You can notice that it is not a Geometric sequence, because:
[tex]\begin{gathered} \frac{-.04}{.04}=-1 \\ \\ \frac{.4}{-.04}=-10 \end{gathered}[/tex]- Using
[tex].004,.0004,.4[/tex][tex]\begin{gathered} \frac{.0004}{.004}=0.1 \\ \\ \frac{4}{.0004}=1,000 \end{gathered}[/tex]Since there is no Common ratio, if you use the value given in the third option, you don't get a Geometric sequence.
- Using this set with the values given in the last option:
[tex].004,.0004,-.0004,.4[/tex]You get:
[tex]\begin{gathered} \frac{.0004}{.004}=0.1 \\ \\ \frac{-.0004}{.0004}=-1 \end{gathered}[/tex]It is not a Geometric sequence.
The answer is: First option.
5/6+1/3×5/8 i need help
We will solve as follows:
[tex]\frac{5}{6}+\frac{1}{3}\cdot\frac{5}{8}=\frac{5}{6}+\frac{5}{24}=\frac{4}{4}\cdot\frac{5}{6}+\frac{5}{24}[/tex][tex]=\frac{20}{24}+\frac{5}{24}=\frac{25}{24}[/tex]can you help me on the part 2 Heads in a Row:
Given:
Flipping a coin twice.
Required:
We need to find the likelihood of flipping heads twice in a row.
Explanation:
The sample space = All possible outcomes.
The sample space, S= {TT,TH,HT,HH}
[tex]n(S)=4[/tex]Let A be the event of flipping heads twice..
The favorable outcomes = flipping heads twice.
The favorable outcomes ={HH}
[tex]n(A)=1[/tex]Consider the probability formula.
[tex]P(A)=\frac{n(A)}{n(S)}[/tex][tex]P(A)=\frac{1}{4}[/tex][tex]P(A)=0.25[/tex]The probability of flipping heads twice in a row is 0.25 which is a close value to the number 0.
This event happens least likely.
Final answer:
Flipping heads twice in a row is the least likely.
The probability of flipping heads twice in a row is 0.25.
5 ptsIn Ms. Johnson's class a student will get 3 points forhaving their name on their paper and 4 points for eachquestion that is correct. In Mr. Gallegos class, a studentwill get 7 points for having their name on their paper and2 points for each question correct. Which inequalitycould be used to determine x, the number of questionsthat would give you a higher grade in Ms. Johnson'sclass?
In Ms. Johnson's class a student will get 3 points for
having their name on their paper and 4 points for each
question that is correct. In Mr. Gallegos class, a student
will get 7 points for having their name on their paper and
2 points for each question correct. Which inequality
could be used to determine x, the number of questions
that would give you a higher grade in Ms. Johnson's
class?
we have
Ms. Johnson's class
3+4x
Mr. Gallegos class
7+2x
so
the inequality is given by
3+4x > 7+2x
solve for x
4x-2x > 7-3
2x>4
x> 2
the number of question must be greater than 2
4(x - 3) - (x - 5) = 0
4(x - 3) - (x - 5) = 0
Solving for x:
4(x - 3) - (x - 5) = 0
4x - 12 - x + 5 = 0
4x - x = 12 - 5
3x = 7
x = 7/3
Answer:
x = 7/3 = 2.33
Junior's brother is 1 1/2 meters tall. Junior is 1 2/5 of his brother's height. How tall is Junior? meters
To determine Junior's height you have to multiply Juniors height by multiplying 3/2 by 7/5his brother's height by 1 2/5.
To divide both fractions, first, you have to express the mixed numbers as improper fractions.
Brother's height: 1 1/2
-Divide the whole number by 1 to express it as a fraction and add 1/2
[tex]1\frac{1}{2}=\frac{1}{1}\cdot\frac{1}{2}[/tex]-Multiply the first fraction by 2 to express it using denominator 2, that way you will be able to add both fractions
[tex]\frac{1\cdot2}{1\cdot2}+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex]Junior's fraction 1 2/5
-Divide the whole number by 1 to express it as a fraction and add 2/5
[tex]1\frac{2}{5}=\frac{1}{1}+\frac{2}{5}[/tex]-Multiply the first fraction by 5 to express it using the same denominator as 2/5, that way you will be able to add both fractions:
[tex]\frac{1\cdot5}{1\cdot5}+\frac{2}{5}=\frac{5}{5}+\frac{2}{5}=\frac{5+2}{5}=\frac{7}{5}[/tex]Now you can determine Junior's height by multiplying 3/2 by 7/5
[tex]\frac{3}{2}\cdot\frac{7}{5}=\frac{3\cdot7}{2\cdot5}=\frac{21}{10}[/tex]Junior's eight is 21/10 meters, you can express it as a mixed number:
[tex]\frac{21}{10}=2\frac{1}{10}[/tex]I would like to ask for Some help on this equation please?
ABC is a right triangle
AB is perpendicular to BC
If 2 lines are perpendicular, the product of slopes is -1
m1 x m2 = -1
mAB x mBC = -1
mAB = -1 / mBC
mAB = -1 / (1/2)
mAB = -2
what are the reasons ? and is there anymore statements
The first reason is GIVEN
If angles ∠XWY and ∠RTU are supplemetary, it means they add up 180°. It demands that lines It demands that lines It demands that
There is sales tax of $9.00 on an item t that costs $ 120.00 before tax. The sales tax on a different item is $ 19.05. How much does the second item cost before tax?
SOLUTION:
Step 1:
In this question, we are given that:
There is sales tax of $9.00 on an item that costs $ 120.00 before tax.
The sales tax on a different item is $ 19.05.
We are meant to find how much the second item cost before tax.
Step 2:
Assuming that there is an equal percentage of tax,
and let the second item cost before tax be y,
then we have that:
[tex]\frac{9}{120}\text{ = }\frac{19.05}{y}[/tex]Cross-multiply, we have that:
[tex]\begin{gathered} 9\text{ x y = 19.05 x 120} \\ 9y\text{ = 2286} \\ \end{gathered}[/tex]Divide both sides by 9, we have that:
[tex]\begin{gathered} y\text{ = }\frac{2286}{9} \\ y\text{ = 254} \end{gathered}[/tex]CONCLUSION:
The cost of the second item before tax = $ 254
6 eggs weigh 3/4 of a pound. How much does each egg weigh? 1/4 pounds1/6 pounds1/8 pounds2/3 pounds
In order for the parallelogram to be a rhombus, x equals?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
parallelogram diagram
Step 02:
geometry:
solve for x:
(5x + 25)° = (12x + 11)°
5x + 25 = 12x + 11
25 - 11 = 12x - 5x
14 = 7x
14 / 7 = x
2 = x
The answer is:
x = 2
how to calculate 1+2?
Suppose that there are two types of tickets to a show: advance and same day. Advance tickets cost 30 and the same day tickets cost 20. For one performance there were 60 tickets sold in all and the total amount paid for them was $1600. How many tickets of each type were sold
Let A be the number of advance tickets sold and S be the total number of same-day tickets sold. The total amount of tickets is A+S, then:
[tex]A+S=60[/tex]The total earnings for A advanced tickets is 30A, while the total earnings for selling S same-day tickets is 20S. Then, the total amount of money for selling A advanced tickets and S same-day tickets, is 30A+20S, then:
[tex]30A+20S=1600[/tex]Solve the system of equations to find the total amount of tickets of each type that were sold. To do so, isolate A from the first equation and then substitute the resulting expression in the second one:
[tex]\begin{gathered} A+S=60 \\ \Rightarrow A=60-S \end{gathered}[/tex][tex]\begin{gathered} 30A+20S=1600 \\ \Rightarrow30(60-S)+20S=1600 \end{gathered}[/tex]Solve for S:
[tex]\begin{gathered} \Rightarrow1800-30S+20S=1600 \\ \Rightarrow1800-10S=1600 \\ \Rightarrow-10S=1600-1800 \\ \Rightarrow-10S=-200 \\ \Rightarrow S=-\frac{200}{-10} \\ \therefore S=20 \end{gathered}[/tex]Substitute S=20 into the expression for A:
[tex]\begin{gathered} A=60-S \\ =60-20 \\ =40 \end{gathered}[/tex]Then, the solution for this system is:
[tex]\begin{gathered} A=40 \\ S=20 \end{gathered}[/tex]2. Assume that each situation can be expressed as a linear cost function and find the appropriate cost function. (a) Fixed cost, $100; 50 items cost $1600 to produce. (b) Fixed cost, $400; 10 items cost $650 to produce. (c) Fixed cost, $1000; 40 items cost $2000 to produce. (d) Fixed cost, $8500; 75 items cost $11,875 to produce. (e) Marginal cost, $50; 80 items cost $4500 to produce. (f)Marginal cost, $120; 100 items cost $15,800 to produce. (g) Marginal cost, $90; 150 items cost $16,000 to produce. (h) Marginal cost, $120; 700 items cost $96,500 to produce.
Given:
Cost function is defined as,
[tex]\begin{gathered} C(x)=mx+b \\ m=\text{marginal cost} \\ b=\text{fixed cost} \end{gathered}[/tex]a) Fixed cost = $100, 50 items cost $1600.
The cost function is given as,
[tex]\begin{gathered} C=\text{Fixed cost+}x(\text{ production cost)} \\ x\text{ is number of items produced} \\ \text{Given that, }50\text{ items costs \$1600} \\ 1600=100\text{+50}(\text{ production cost)} \\ \text{production cost=}\frac{1600-100}{50} \\ \text{production cost}=30 \end{gathered}[/tex]So, the cost function is,
[tex]C=30x+100[/tex]b) Fixed cost = $400, 10 items cost $650.
[tex]\begin{gathered} 650=400+10p \\ 650-400=10p \\ p=25 \\ \text{ Cost function is,} \\ C=25x+400 \end{gathered}[/tex]c) Fixed cost= $1000, 40 items cost $2000 .
[tex]\begin{gathered} 2000=1000+40p \\ p=25 \\ C=25x+1000 \end{gathered}[/tex]d) Fixed cost = $8500, 75 items cost $11,875.
[tex]\begin{gathered} 11875=8500+75p \\ 11875-8500=75p \\ p=45 \\ C=45x+8500 \end{gathered}[/tex]e) Marginal cost= $50, 80 items cost $4500.
In this case we know the value of m = 50 .
Use the slope point form,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(80,4500) \\ y-4500=50(x-80) \\ y=50x-4000+4500 \\ y=50x+500 \\ C=50x+500 \end{gathered}[/tex]f) Marginal cost=$120, 100 items cost $15,800.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(100,15800) \\ y-15800=120(x-100) \\ y=120x-12000+15800 \\ y=120x+3800 \\ C=120x+3800 \end{gathered}[/tex]g) Marginal cost= $90,150 items cost $16,000.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(150,16000) \\ y-16000=90(x-150) \\ y=90x-13500+16000 \\ y=90x+2500 \\ C=90x+2500 \end{gathered}[/tex]h) Marginal cost = $120, 700 items cost $96,500
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(700,96500) \\ y-96500=120(x-700) \\ y=120x-84000+96500 \\ y=120x+12500 \\ C=120x+12500 \end{gathered}[/tex]Write the percent as fraction or mixed number in simplest form 750%
Answer
[tex]7\frac{1}{2}[/tex]Explanation
The 750 percent as a fraction or mixed number in simplest form is calculated as follows:
[tex]750\%=\frac{750}{100}=\frac{75}{10}=\frac{15}{2}=7\frac{1}{2}[/tex]a leaky faucet drips 5 teaspoons of water every 3 hours how long will it take the leaky faucet to drip 75 teaspoons of water
∵ 5 teaspoons of water dropped every 3 hours
∵ We need to find the time taken for 75 teaspoons
→ By using the ratio method
→ Time: teaspoons
→ 3 : 5
→ h : 75
→ By using cross multiplication
∵ 5 x h = 3 x 75
∴ 5h = 225
→ Divide both sides by 5 to find h
∴ h = 45
It will take 45 hours
Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.) 9 + 4 + (-1) + ... + (-536)
SOLUTION
The terms below make an A.P. Now we are told to find the sum of the AP.
Sum of an AP is given by
[tex]S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack}[/tex]Where S = sum of the AP, a = first term = 9, d = -5, n= ?
So we have to find n first before we can find the sum. The nth term which is the last term = -536. So we will use it to find the number of terms "n"
[tex]\begin{gathered} \text{From T}_{n\text{ }}=\text{ a +(n-1)d where T}_{n\text{ }}=\text{ -536} \\ -536\text{ = 9+(n-1)-5} \\ -536\text{ = 9-5n+5} \\ -536\text{ = 14-5n} \\ -5n\text{ = -536-14} \\ -5n\text{ = -550} \\ n\text{ = 110} \end{gathered}[/tex]Now let's find the sum
[tex]\begin{gathered} S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack} \\ S\text{ = }\frac{110}{2}\lbrack2\times9\text{ + (110-1)-5\rbrack} \\ S\text{ = 55\lbrack{}18+(119)-5\rbrack} \\ S\text{ = 55\lbrack{}18 - 595\rbrack} \\ S\text{ = 55}\times-577 \\ S\text{ = -31735} \end{gathered}[/tex]Therefore, the sum = -31735
complete the table of ordered pairs for the linear equation. 5x+8y=3
Given:
5x+8y=3
The objective is to fill the table using the given values of x otr y.
Let's take that, x=0 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5(0)+8y=3 \\ 0+8y=3 \\ y=\frac{3}{8} \end{gathered}[/tex]Hence, the the required solution will be (0,3/8).
Let's take that, y=0 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5x+8(0)=3 \\ 5x+0=3 \\ x=3-5 \\ x=-2 \end{gathered}[/tex]Hence, the the required solution will be (-2,0).
Let's take that, y=1 and substitute in the given equation.
[tex]\begin{gathered} 5x+8y=3 \\ 5x+8(1)=3 \\ 5x+8=3 \\ 5x=3-8 \\ 5x=-5 \\ x=-\frac{5}{5} \\ x=-1 \end{gathered}[/tex]Hence, the the required solution will be (-1,1).
i need help solving this and also what does the 2 that's on the top of some letters mean
given the expression :
[tex]a-bc^2[/tex]We need to evaluate the expression when :
[tex]\begin{gathered} a=3 \\ b=2 \\ c=-1 \end{gathered}[/tex]So, substitute with a , b and c at the expression
The result will be :
[tex]\begin{gathered} a-bc^2 \\ =3-2\cdot(-1)^2 \\ =3-2\cdot1 \\ =3-2 \\ \\ =1 \end{gathered}[/tex]There is another expression :
[tex]c^2+a^2b[/tex]By substitute with the values of a, b and c
so, the result will be :
[tex]\begin{gathered} c^2=(-1)^2=1 \\ a^2=3^2=9 \\ \\ c^2+a^2b=1+9\cdot2=1+18=19 \end{gathered}[/tex]The area (in square inches) of a rectangle is given by the polynomial function A(b)=b^2 +9b+18. If the width of the rectangle is (b+3) inches what is the length?
As given by the question
There are given that area of rectangle and width of a rectangle
[tex]\begin{gathered} \text{Area}=A(b)=b^2+9b+18 \\ \text{Width}=(b+3) \end{gathered}[/tex]Now,
From the formula of area of a rectangle:
[tex]\text{Area}=\text{length}\times width[/tex]Then,
Put the value of an area and width into the above formula
So,
[tex]\begin{gathered} \text{Area}=\text{length}\times width \\ b^2+9b+18=length\times(b+3) \end{gathered}[/tex]Then,
[tex]\begin{gathered} b^2+9b+18=length\times(b+3) \\ (b+3)(b+6)=\text{length}\times(b+3) \\ \text{length}=\frac{(b+3)(b+6)}{(b+3)} \\ \text{length}=(b+6) \end{gathered}[/tex]Hence, the value of length is ( b + 6 ).
i have already graphed the problem, please help me fill in the following.
ANSWER
There are 3 major points to prove that a quadrilateral is a rhombus
1. Indicate that the diagonals of the shape are bisectors that are perpendicular to each other
2. Indicate that the diagonal of the shape bisects both pair of opposite angles
3. Indicate that the shape is a parallelogram with sides of the same length
A triangular banner has an area 2000 square yards. Find the measures of the base and height of the triangle if the base is five-eighths of the height. What are the units of measurement.
ANSWER:
Height = 80 yds
Base = 50 yds
STEP-BY-STEP EXPLANATION:
Given:
Area = 2000 square yards
Height = h
Base = 5/8h
We can calculate the value of the height using the triangle area formula, just like this:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{ We replacing} \\ 2000=\frac{h\cdot \frac{5}{8}h}{2} \\ h^2=\frac{2000\cdot2\cdot8}{5} \\ h=\sqrt{6400} \\ h=80\text{ yd} \\ \text{ therefore, the base is:} \\ b=\frac{5}{8}\cdot80 \\ b=50\text{ yd} \end{gathered}[/tex]Height = 80 yds
Base = 50 yds
Use the figure below to find the value of x. (x + 20) y (x + 10° (y – 40)
Answer:
The value of x is 75;
[tex]x=75[/tex]Explanation:
From the diagram;
[tex](x+20)^0+(x+10)^0=180^0[/tex]Reason; supplementary angles.
Solving the equation, we have;
[tex]\begin{gathered} x+x+20+10=180 \\ 2x+30=180 \\ 2x=180-30 \\ 2x=150 \\ x=\frac{150}{2} \\ x=75 \end{gathered}[/tex]Therefore, the value of x is 75;
[tex]x=75[/tex]22The value of the hypotenuse in the right triangle shown isinches.14 in48 inFigure not drawn to scale
SOL
Step 1 :
In this question, we are meant to find the value of
the hypotenuse in the right angle below:
Before, we proceed, we still need to remind ourselves of Pythagoras' theorem,
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Step 2 :
From the above theorem, we can see that that the two adjacent sides are :
14 inches and 48 inches.
From the principle of Pythagoras' Theorem,
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{where a = 14 inches} \\ b\text{ = 48 inches} \\ c^2=14^2+48^2 \\ c^2\text{ = ( 14 x 14 ) + ( 48 x 48 )} \\ c^2\text{ = 196 + 2304} \\ c^2\text{ = 2500} \\ \text{square root both sides, we have that :} \\ c\text{ = 50 inches} \end{gathered}[/tex]
CONCLUSION :
The value of the hypotenuse in the Right angle, c = 50 inches.
What is the value of y in the solution set of the system of linear equations shown below?y = -x + 124x - 2y = 36A.10B. 8C. 6D. 2
y = 2 (option D)
Explanation:y = -x + 12
4x - 2y = 36
rewriting the equations:
y + x = 12 ....equation 1
-2y + 4x = 36 ....equation 2
Using elimination method:
we will be eliminating y. So we need to make the coefficient of y to be the same in both equation. We will be multiplying the first equation by 2.
2y + 2x = 24 ....equation 1
-2y + 4x = 36 ....equation 2
Add both equations:
2y + (-2y) + 2x + 4x = 24 + 36
2y-2y + 6x = 60
6x = 60
x = 60/6 = 10
Insert the value of x in any of the equation. Using equation 2:
4(10) - 2y = 36
40 -2y = 36
-2y = 36 - 40
-2y = -4
y = -4/-2
y = 2 (option D)
Determine the transformations that produce the graph of the functions g (T) = 0.2 log(x+14) +10 and h (2) = 5 log(x + 14) – 10 from the parent function f () = log 1. Then compare the similarities and differences between the two functions, including the domain and range. (4 points)
The transformation to get g(x) from f(x) are:
translate 14 units to the left and 10 unit upwards
[tex]h(x)=5\log (x+14)-10[/tex]the transformatio to get h(x) from f(x) are:
translate 14 units to the left and 10 units downwards
Write the equation of a line that is parallel to y = 1/2x -4 and that passes through the point (9, -6)
The most appropriate choice for equation of line in slope intercept form will be given by-
[tex]y = \frac{1}{2}x - \frac{21}{2}[/tex] is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by [tex]y = mx + c[/tex]
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line
Here,
The given equation of line is [tex]y = \frac{1}{2} x - 4[/tex]
Slope of this line = [tex]\frac{1}{2}[/tex]
Slope of the line parallel to this line = [tex]\frac{1}{2}[/tex]
The line passes through (9 , -6)
Equation of the required line =
[tex]y - (-6) = \frac{1}{2}(x - 9)\\2y + 12 = x - 9\\2y = x - 9 -12\\2y = x -21\\y = \frac{1}{2}x - \frac{21}{2}[/tex]
To learn more about equation of line in slope intercept form, refer to the link-
https://brainly.com/question/25514153
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