Given:
Given the equation
[tex]2x-\frac{1}{4}y=1[/tex]Required: Solve for y.
Explanation:
Subtract 2x on both sides.
[tex]\begin{gathered} 2x-\frac{1}{4}y-2x=1-2x \\ -\frac{1}{4}y=1-2x \end{gathered}[/tex]Multiply both sides by -4.
[tex]\begin{gathered} y=-4(1-2x) \\ =4(2x-1) \end{gathered}[/tex]Final Answer: y = 4(2x - 1)
Find the slope of the line?Ordered pairs (-4, 1) and (1, -2)
The slope of the line is:
[tex]m=-\frac{3}{5}[/tex]To find the slope of a line with two points, P and Q, the formula is:
[tex]\begin{gathered} P=(x_p,y_p);Q=(x_q,y_q) \\ m=\frac{y_p-y_q}{x_p-x_q} \end{gathered}[/tex]Then if P = (-4, 1) and Q = (1, -2)
We can replace inthe formula:
[tex]m=\frac{1-(-2)}{-4-1}=-\frac{3}{5}[/tex]A card is drawn from a deck of 52 cards. What is the probability that it is a numbered card (2-10) or a heart?
we know that
Total cards=52
Total numbered card (2-10)=36
Total heart=13
numbered card and heart=9
therefore
The probability is equal to
P=(36+13-9)/52
P=40/52
P=20/26=10/13
The answer is 10/13A company orders business cards for their employees. The company pays $9.00 per 100 cards ordered. The company orders2,000 business cards for Karen and 2,500 business cards for Lamar. How much more do the business cards for Lamar cost than thebusiness cards for Karen?$9$45$450d $500
Take into account what the company pays per 100 cards ordered, which is $9.00.
To determine the cost of the cards for Karen and Lamar
write an equation and solvefour times the complement of an angle is 40° lessthan twice the angles supplement. Find the angle,its complement, and its supplement
Let the angle be 'x' degrees.
The complement (C) of the corresponding angle will be,
[tex]C=90-x[/tex]And the supplement (S) of the corresponding angle will be,
[tex]S=180-x[/tex]According to the condition given in the problem,
[tex]4C=2S-40^{}[/tex]Substitute the values,
[tex]\begin{gathered} 4(90-x)=2(180-x)-40 \\ 360-4x=360-2x-40 \\ -4x=-2x-40 \\ 4x-2x=40 \end{gathered}[/tex]Simplify the expression further,
[tex]\begin{gathered} 2x=40 \\ x=\frac{40}{2} \\ x=20 \end{gathered}[/tex]Substitute this value of 'x' to obtain the complement and supplement angles as follows,
[tex]\begin{gathered} C=90-20=70 \\ S=180-20=160 \end{gathered}[/tex]Thus, the angle measures 20 degrees, its complement measures 70 degrees, while its supplement measures 160 degrees.
3. f(x) = |-3x - 1|3. For this function, findeach of the following:a. f(-1)b. f(0)c. f(3)
Given the absolute function;
[tex]f(x)=|-3x-1|[/tex](a)
[tex]\begin{gathered} f(-1)=|-3x-1| \\ f(-1)=|-3(-1)-1| \\ f(-1)=|3-1| \\ f(-1)=|2| \\ f(-1)=2 \end{gathered}[/tex](b)
[tex]\begin{gathered} f(0)=|-3(0)-1| \\ f(0)=|0-1| \\ f(0)=|-1| \end{gathered}[/tex]Here, we recall the absolute rule that;
[tex]|-a|=a[/tex]Thus, we have;
[tex]f(0)=|-1|=1[/tex](c)
[tex]\begin{gathered} f(3)=|-3(3)-1| \\ f(3)=|-9-1| \\ f(3)=|-10| \\ f(3)=10 \end{gathered}[/tex]Teachers' Salaries The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680Find the probabilities.P (X>45,500)
What is the probability of drawing a jack from a standard deck of cards, replacing it,shuffling, then drawing an ace?
- We have 52 cards in a deck of cards.
- We have 4 cards of the same number (4 jack, 4 aces...).
Probability of drawing a jack = 4/52
Probability of drawing a jack followed by an ace =(4/52)*(4/52)=0.00592
Refer to the rectangle ABCD, shown below, where m(<4)=10degrees. Need help.
From the statement of the problem, we know that:
[tex]m(\angle4)=18^{\circ}\text{.}[/tex]From the diagram, we see that:
1) ∠1 and ∠4 are complementary angles, so they sum up 90°:
[tex]\begin{gathered} m\mleft(\angle1\mright)+m\mleft(\angle4\mright)=90\degree \\ m\mleft(\angle1\mright)=90\degree-m\mleft(\angle4\mright), \\ m(\angle1)=90\degree-18^{\circ}=72^{\circ}\text{.} \end{gathered}[/tex]2) ∠4, ∠3 and a right angle are inner angles of a triangle, so they must sump up 180°:
[tex]\begin{gathered} m(\angle4)+m(\angle3)+90^{\circ}=180^{\circ}\text{.} \\ m(\angle3)=180^{\circ}-90^{\circ}-m(\angle4), \\ m(\angle3)=180^{\circ}-90^{\circ}-18^{\circ}=72^{\circ}\text{.} \end{gathered}[/tex]3) ∠3 and ∠2 are complementary angles, so they sum up 90°:
[tex]\begin{gathered} m(\angle3)+m(\angle2)=90^{\circ}, \\ m(\angle2)=90^{\circ}-m(\angle3), \\ m(\angle2)=90^{\circ}-72^{\circ}=18^{\circ}\text{.} \end{gathered}[/tex]Answer
c. m(∠1) = 72°, m(∠2) = 18°, m(∠3) = 72°.
How much water must be evaporated from 8 grams of a 30% antiseptic solution to produce a 40% solution?
Answer:
Step-by-step explanation:
8 grams of 30% --> 2.4 grams of AS For 2.4 grams to be 40% --> 6 grams of solution Evaporate 2 grams of water
Find the reference angle of [tex] \frac{ - 13\pi}{6} [/tex]
Reference angle
The reference angle of a given angle A is the acute angle that A forms with the x-axis
We need to calculate the reference angle of
[tex]\frac{ - 13\pi}{6}[/tex]This angle is greater than any angle of a single turn on the trigonometric circle.
Let's convert the improper fraction to a mixed fraction:
[tex]-\frac{13\pi}{6}=-2\pi-\frac{\pi}{6}[/tex]-2π corresponds to a complete turn around the circle, so we can discard that part and take only the -π/6
Since it's a negative angle, it runs clockwise and is located at the IV quadrant. The reference angle is π/6 because it's the angle it forms with the x-axis.
We'll include an image of the angle below
In windy cold weather, the increased rate of heat loss makes the temperature feel colder than the actual temperature. To describe an equivalent temperature that more closely matches how it “feels,” weather reports often give a windchill index, WCI. The WCI is a function of both the temperature F(in degrees Fahrenheit) and the wind speed v (in miles per hour). For wind speeds v between 4 and 45 miles per hour, the WCI is given by the formula(FORMULA SHOWN IN PHOTO)A) What is the WCI for a temperature of 10 F in a wind of 20 miles per hour?B) A weather forecaster claims that a wind of 36 miles per hour has resulted in a WCI of -50 F. What is the actual temperature to the nearest degree?
Let's remember what the variables mean:
F= temperature (in Fahrenheit),
v= wind speed.
A) The formula "works" when the wind speed is between 4 and 45 miles per hour. The question asks for a wind speed of 20 miles per hour. Then, we can apply the formula. Here,
[tex]\begin{cases}F=10 \\ v=20\end{cases}[/tex]Then,
[tex]\begin{gathered} WCI(10,20)=91.4-\frac{(10.45+6.69\cdot\sqrt[]{20}-0.447\cdot20)(91.4-10)}{22}\approx\ldots \\ \ldots91.4-116.2857=-24.8857 \end{gathered}[/tex]Approximating, the answer is
[tex]-25F[/tex]B) This question is just about to find F in the provided equation after replacing the given v and WCI. Let's do that:
[tex]\begin{gathered} -50=91.4-\frac{(10.45+6.69\cdot\sqrt[]{36}-0.447\cdot36)(91.4-F)}{22}, \\ -141.4=-\frac{(10.45+6.69\cdot\sqrt[]{36}-0.447\cdot36)(91.4-F)}{22}, \\ -3110.8=-(10.45+6.69\cdot\sqrt[]{36}-0.447\cdot36)(91.4-F), \\ 3110.8=(10.45+6.69\cdot\sqrt[]{36}-0.447\cdot36)(91.4-F), \\ \frac{3110.8}{10.45+6.69\cdot\sqrt[]{36}-0.447\cdot36}=91.4-F, \\ F=91.4-\frac{3110.8}{10.45+6.69\cdot\sqrt[]{36}-0.447\cdot36}\approx1.2 \end{gathered}[/tex]Then, the actual temperature is
[tex]1F[/tex]Solve for x in the equation below:3(x - 5) = 5x - (3 - x)
Step 1: We have the following equation:
3(x - 5) = 5x - (3 - x)
Step 2: Solve the parentheses
3x - 15 = 5x - 3 + x
Step 3: Like terms
3x - 5x -x = - 3 + 15
-3x = 12
Step 4: Dividing by -3 at both sides
-3x/-3 = 12/-3
x = -4
Step 5: Let's prove the answer is correct
3 (-4 - 5) = 5 * -4 - (3 - -4)
3 (-9) = -20 -3 - 4
-27 = - 27
The solution is correct
Using the order of operations, which operation should you perform last to evaluate the expression below?(7*4)+(10 ÷ 2)*(14.7 - 9)A.multiplicationB.divisionC.additionD.subtractionHELP! A.P.S
Explanation
Given (7*4)+(10 ÷ 2)*(14.7 - 9), we can see that only two operations occur outside of the parenthesis which is multiplication and addition.
In the order of evaluation of expressions, the parenthesis comes first before multiplication and then addition. Therefore,
Answer: Option C (Addition)
I need help to find the indicated operation:g(x)= -x^2 +4xh(x)= -4x-1Find (3g-h)(-3)
We have the following functions:
[tex]\begin{gathered} g\mleft(x\mright)=-x^2+4x \\ h\mleft(x\mright)=-4x-1 \end{gathered}[/tex]And we need to find:
[tex](3g-h)(-3)[/tex]Step 1. Find 3g by multiplying g(x) by 3:
[tex]\begin{gathered} g(x)=-x^2+4x \\ 3g=3(-x^2+4x) \end{gathered}[/tex]Use the distributive property to multiply 3 by the two terms inside the parentheses:
[tex]3g=-3x^2+12x[/tex]Step 2. Once we have 3g, we subtract h(x) to it:
[tex]3g-h=-3x^2+12x-(-4x-1)[/tex]Here we have 3g and to that, we are subtracting h which in parentheses.
Simplifying the expression by again using the distributive property and multiply the - sign by the two terms inside the parentheses:
[tex]3g-h=-3x^2+12x+4x+1[/tex]Step 4. Combine like terms:
[tex]3g-h=-3x^2+16x+1[/tex]What we just found is (3g-h)(x):
[tex](3g-h)(x)=-3x^2+16x+1[/tex]Step 5. To find what we are asked for
[tex]\mleft(3g-h\mright)\mleft(-3\mright)[/tex]We need to evaluate the result from step 4, when x is equal to -3:
[tex](3g-h)(-3)=-3(-3)^2+16(-3)+1[/tex]Solving the operations:
[tex](3g-h)(-3)=-3(9)^{}-48+1[/tex][tex](3g-h)(-3)=-27^{}-48+1[/tex][tex](3g-h)(-3)=-74[/tex]Answer:
[tex](3g-h)(-3)=-74[/tex]for #5 solve for x. then find the missing piece(s) of parallelogram.
Answer:
Given that,
From the parallelogram, the opposite sides of the parallelogram are -2+4x and 3x+3
Explanation:
From the properties of parallelogram, we have that
Opposite sides of a parallelogram are equal
We get,
[tex]-2+4x=3x+3[/tex]Solving we get,
[tex]4x-3x=3+2[/tex][tex]x=5[/tex]Answer is :x=5
Find the volume of cylinder with r=25.5 ft and height=45ft use 3.14 for pi. Round the answer to the nearest hundredth
The Volume of a Cylinder
Given a cylinder of base radius r and height h, its volume is calculated as follows:
[tex]V=\pi r^2h[/tex]We have a cylinder with dimensions r = 25.5 ft and h = 45 ft. Substituting the values in the formula:
[tex]V=\pi\cdot25.5^2\cdot45[/tex]Using π = 3.14:
[tex]\begin{gathered} V=3.14\cdot650.25ft^2\cdot45ft \\ V=91,880.325ft^3 \end{gathered}[/tex]Rounding to the nearest hundredth:
V = 91,880.33 cubic ft
A Parks and Recreation department in a small city conducts a survey to determine what recreational activities for children it should offer. Of the 1200 respondents,400 parents wanted soccer offered625 parents wanted baseball/softball offered370 parents wanted tennis offered150 parents wanted soccer and tennis offered315 parents wanted soccer and baseball/softball offered230 parents wanted baseball/softball and tennis offered75 parents wanted all three sports offeredHow many parents didn’t want any of these sports offered?a) 155b) 75c) 0d) 425
There were 1200 respondents:
400 parents wanted soccer offered
370 parents wanted tennis offered
625 parents wanted baseball/softball offered
150 parents wanted soccer and tennis offered
315 parents wanted soccer and baseball/softball offered
230 parents wanted baseball/softball and tennis offered
75 parents wanted all three sports offered
Therefore:
We have to add all the options that were mixed with different sports:
150 + 315 + 230 = 695 - 75= 620 (We subtract 75 because it's already included in the other values as we can see in the diagram)
We have to add all the parents that chose only one sport:
400 + 370 + 625= 1395
We have to subtract 620 from 1395:
1395 - 620= 775 parents who chose any sport
Now:
1200 - 775 = 425 respondents who didn't want any.
Therefore, 425 parents didn't want any of the sports offered.
The answer is D) 425.
determine if the following equations represent a linear function if so write it in standard form Ax+By=C9x+5y=102y+4=6x
9x + 5y = 10
is a linear equation because all variables are raised to exponent 1.
This equation is already written in standard form (A = 9, B = 5, C = 10)
2y + 4 = 6x
is a linear equation because all variables are raised to exponent 1.
Subtracting 2y at both sides:
2y + 4 - 2y= 6x - 2y
4 = 6x - 2y
or
6x - 2y = 4
which is in standard form (A = 6, B = -2, C = 4)
=Given f(x) = -0.4x – 10, what is f(-12)? If it does not exist,enter DNE.
We have the function:
[tex]f\mleft(x\mright)=-0.4x-10[/tex]And we need to find its value when x = -12. So, replacing x with -12, we obtain:
[tex]f(-12)=-0.4(-12)-10=4.8-10=-5.2[/tex]Notice that the product of two negative numbers is a positive number.
Therefore, the answer is -5.2.
Can you tell me if im right or wrong
I will begin typing in the answer tab. It will take me approximately _
This question is from a MATH extra credit assignment, so unless I accidentally clicked on a subject other than maths... This question is also not from a test. Please help me if you can. Thank you if you do :)
Answer
$6,314
Step-by-step explanation
Compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
• A: final amount, in dollars
,• P: principal, in dollars
,• r: interest rate, as a decimal
,• n: number of times interest is applied per year
,• t: time in years
In this case, the investment is compounded annually, that is, once per year (n = 1). Substituting P = $4,625, r = 0.0352 (=3.52/100), n = 1, and t = 9 years, we get:
[tex]\begin{gathered} A=4,625(1+\frac{0.0352}{1})^{1\cdot9} \\ A=4,625(1.0352)^9 \\ A=\text{ \$}6,314 \end{gathered}[/tex]factor completely5r^3-10r^2+3r-6
You have the following polynomial:
5r³ - 10r² + 3r - 6
In order to factorize the given polynomial, use synthetic division:
5 -10 3 -6 | 2
10 0 6
5 0 3 0
The remainder is zero in the previous division, then, r - 2 is a factor of the given polynomial, the other factor is formed with the coefficients of the division, just as follow:
5r³ - 10r² + 3r - 6 = (r - 2)(5r² + 3)
Hence, the factor are (r - 2)(5r² + 3)
Answer:(r-2) x (5r^2+3)
Step-by-step explanation:
The number of chaperones on a field trip must include 1 teacher for every 4 students, plus 2 parents total. The function describing the number of chaperones for a trip of x students is f(x) = 1/4x + 2.
a. How will the graph change if the number of parents is reduced to 0?
b. How will the graph change if the number of teachers is raised to 1 for every 3 students?
Number of chaperones for a trip defined by function f(x) = (1/4)x+2 then,
a. If the parents is reduced to 0 then the graph passes through origin (0,0).
b. If the number of teachers is raised to 1 for every 3 students then line cut x-axis at (-6,0) .
As given in the question,
Given conditions:
Field trip must include 1 teacher for every 4 students and add 2 parents in total.
Number of chaperones for a trip defined by function f(x) = (1/4)x+2
a. If the parents is reduced to 0 then the changes seen in the graph are as follow:
f(x) = (1/4)x+2 passes through the point (0,2)
when parents changes to 0 then graph passes through (0,0).
b. If the number of teachers is raised to 1 for every 3 students then the changes seen in the graph are as follow:
For f(x) = (1/4)x+2 the graph cut axis at (-8,0)
When for every 1 teacher there are 3 students then graph cut x-axis at (-6,0).
Therefore, number of chaperones for a trip defined by function f(x) = (1/4)x+2 then,
a. If the parents is reduced to 0 then the graph passes through origin (0,0).
b. If the number of teachers is raised to 1 for every 3 students then line cut x-axis at (-6,0) .
Learn more about function here
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Yasmin went to the store and bought 3 and 1/2 pounds of ground beef for 11:20 how much do the ground beef cost per pound
Yasmin bought 3 1/2 pounds of ground beef, we can express the amount that she bought as a fraction like this:
[tex]3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{6+1}{2}=\frac{7}{2}[/tex]Since she bought it for $11.2, if we divide the cost by the amount that she purchased, we get the cost per pound, like this:
[tex]\frac{11.2}{\frac{7}{2}}[/tex]To divide by a fraction, we just have to invert its numerator and denominator:
[tex]\frac{11.2}{\frac{7}{2}}=11.2\times\frac{2}{7}=\frac{22.4}{7}=3.2[/tex]Then, the cost per pound equals $3.2
Maxim has been offered positions by two car companies. The first company pays a salary of $12000 plus a commission of $800 for each car sold. The second pays a salary of $15600 plus a commission of $600 for each car sold. How many cars would need to be sold to make the total pay the same?
To make the total pay the same, 18 cars would need to be sold
Explanation:Let the number of cars sold be x
The first company pays a salary of $12000 plus a commission of $800 for each car sold
Total pay for the first company = 12000 + 800x
The second pays a salary of $15600 plus a commission of $600 for each car sold
Total pay for the second company = 15600 + 600x
If the total pay is the same:
12000 + 800x = 15600 + 600x
800x - 600x = 15600 - 12000
200x = 3600
x = 3600/200
x = 18
To make the total pay the same, 18 cars would need to be sold
In the triangle below, suppose that mZW=(x+4)º, mZX=(5x-4)°, and mLY= (4x)".Find the degree measure of each angle in the triangle.
can you please find the slope and the y intersept of the graph of the linear equation y= 4x-5
the slope of the linear equation is 4 and the y intercept is -5
Explantion:we apply the equation of line to find the slope and intercept
Equation of line is in the form: y = mx + c
where m = slope and c = y - intercept
comparing the given equation with the equation of line:
linear equation y= 4x-5
y = y
4x - 5 = mx + c
This means m = 4
4x = mx
m = 4
-5 = c
Hence, the slope of the linear equation is 4 and the y intercept is -5
You go to the pet store with $25. You decide to buy 2 fish for $3.69 each and fish foos for $4.19. Rounded tanks are $11.48 square-shaped tanks are $14.89. Estimate your total cost to find which tank you can can buy. About how much money will you have left?
Answer: you will only have enough money for the rounded tank, after buying everything you will have 9 cents left
Step-by-step explanation: two $3.69 fish, $4.19 fish food. 2x3.69=7.38+4.19=11.57
25-11.57=13.43
13.43+11.48=24.91
25-24.91=0.09
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
7. Which expression is equivalent to the distance between -2 and -15 on a number line? Select all that apply. OT-15 - (-2)] O 1-15-2 O 1-15+ (-2) 1-2 + (-15) 1-2-(15)