Equation of a line that has a slope of 4 and passes through point (1, 6) is y = 4x + 2 . Hence, C is the correct option.
What is equation of the line?To represent the standard form of equation of a line are:
Slope-intercept form:
y = mx + c
Here m represent the slope of the given line and c is the y intercept.
Intercept form:
x/a + y/b = 1
Generic way of representing the straight line, i.e. Ax+By+C = 0
x/(-C/A) + y/(-C/B) = 1
Hence a = -C / A and b = – C / B
Normal form:
The equation of the line whose length of the normal from the origin is p and the angle made by the normal with the positive x-axis is given by α is given by:
x cos α+y sin α = p
General equation of the line is represented in the form:-
y - y1 = m (x-x1) ,
Where x1, y1 represents a point on the line whereas,
m represents the slope of the line.
= (1 , 6) point on the line
= Slope (m) = 4
Putting all the required values in general equation:-
y - 6 = 4 ( x-1 )
Hence, we get y = 4x + 2
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KT's Restaurant has contracted with the Vidalia Times for
5,000 column inches in daily newspapers and 10,000
column inches in the Saturday newspaper. Daily column
inches are $27.55, and Saturday rates are $29.35 per
column inch. How much should KT's Restaurant budget for
newspaper advertising for the coming year?
The budget of KT's Restaurant for newspaper advertising for the coming year is $58,533,500
Given,
The length of advertisement of KT's Restaurant in Vidalia Times in week days = 5,000
The length of advertisement of KT's Restaurant in Vidalia Times in Saturdays = 10,000
The cost of daily column = $27.55 per column inch
The cost of Saturdays = $29.35 per column inch
We have to find the budget of KT's Restaurant for newspaper advertising for the coming year;
Here,
There are approximately 53 Saturdays in a year.
So,
365 - 53 = 312
Then,
The budget of advertisement on daily column = 312 × 5000 × 27.55 = $42,978,000
The budget of advertisement on Saturday column = 53 × 10,000 × 29.35 = $1,555,500
Therefore,
The total budget for advertisement = 42,978,000 + 1,555,500 = $58,533,500
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(−3,y) and (x,2).
y=4x+6
orderd pair
The values of x and y are -1 and 6 respectively, this forms an ordered pair of (-3,6) and (-1,2).
What are the missing x and y values values of the given ordered pair?Given the equation and ordered pair in the question;
y = 4x + 6Point: (-3,y) Point; (x,2)Find the y-value by substituting the x-value into the equation and solving for y.
y = 4x + 6
Plug in x = -3
y = 4( -3 ) + 6
y = -12 + 6
y = 6
Find the x-value by substituting the y-value into the equation and solving for x.
y = 4x + 6
Plug in y = 2
2 = 4x + 6
2 - 6 = 4x
-4 = 4x
x = -4/4
x = -1
Therefore, the ordered pair are (-3,6) and (-1,2).
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Please HELP 7 B(x)*C(x)
Answer: dont be rude
Step-by-step explanation:
1 10 points
The rule for dilation of a quadrilaterial is Do.0.08 (z,y) (0.08z, 0.08y). What is the Y coordinate of a new point if the new coordinate is (3-9)? Round to the nearest
hundredth if necessary.
Type your answer.....
2
10 points
Answer:
Step-by-step explanation:
The rule for dilation of a quadrilaterial is Do.0.08 (z,y) (0.08z, 0.08y). What is the Y coordinate of a new point if the new coordinate is (3-9)? Round to the nearest
hundredth if necessary
If the pediatric floor of the hospital has 165 beds how many rooms are there if each room holds 3 beds?
(2x²-3x+1)-(-x² + 2x − 2) - (2x - 3)² =
Answer:
6x^2-17x+12
Step-by-step explanation:
Distribute
2x^2-3x+1+x^2-2x+2(-2x+3)^2
Square (2x+3)
(-2x+3)(-2x+3)
FOIL
4x^2-6x-6x+9
Combine like terms
4x^2-12x+9
re-write equation
2x^2-3x+1+x^2-2x+2+4x^2-12x+9
Combine like terms
6x^2-17x+12
Please help me to solve this simple question.
I will mark your answer brainliest!
Answer:
4/3
Step-by-step explanation:
You want the limit as t→1 of (t³+t²-5t+3)/(t³-3t+2).
Simplified formThe fact that each polynomial evaluates to 0 at t=1 tells you that (t-1) is a factor of each. Factoring that out gives ...
[tex]\dfrac{t^3+t^2-5t+3}{t^3-3t+2}=\dfrac{(t-1)(t^2+2t-3)}{(t-1)(t^2+t-2)}=\dfrac{(t-1)(t-1)(t+3)}{(t-1)(t-1)(t+2)}\\\\=\dfrac{t+3}{t+2}[/tex]
The limit at t = 1 is found by direct substitution:
lim = (1 +3)/(1 +2) = 4/3
5. During the 2016 presidential election, 58.1% of eligible voters participated. In a recent poll of 1048 randomly selected
eligible voters, 586 responded that they intend to vote.
(a) Test at the 5% significance level if the percent of eligible voters that intend to participate is different from the 2016
participation rate.
(b) Explain a Type II error in the context of the data.
Using the z-distribution to test the hypothesis, it is found that:
a) The conclusion is that there is not enough evidence to conclude that the percentage has changed from 2016.
b) A Type II error would mean finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is the same as in 2016, that is:
[tex]H_0: p = 0.581[/tex]
At the alternative hypothesis, it is tested if the proportion is different, hence:
[tex]H_1: p \neq 0.581[/tex]
A Type II error is the non-rejection of a false null hypothesis, that is, finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.
What is the test statistic?The equation calculating the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the variables are listed as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the value for these variables is given as follows:
[tex]\overline{p} = \frac{586}{1048} = 0.559, n = 1048, p = 0.581[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.559 - 0.581}{\sqrt{\frac{0.581(0.419)}{1048}}}[/tex]
z = -1.44.
The critical value for a two-tailed test is with a significance level of 0.05 is:
|z| = 1.96.
The absolute value of the test statistic is of |z| = 1.44 < 1.96, meaning that there is not enough evidence to conclude that the percentage has changed from 2016.
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What is the size of angle x?
Write a justification for your answer.
The angle x will be 34°.
From the properties of circles we get to know that the angle at the center and the angle between two tangents are always supplementary.
Supplementary angles are those which always sum to to 180°.
For example ∠HJK is supplementary to ∠HIK the their sum will come out to be 180°.
similarly ∠ROP + ∠RQP = 180°
∠RQP = 180° - ∠ROP
∠ROP is given to us 146°
After putting it in the equation above we get ∠RQP = 34°
Therefore x comes out to be 34°.
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wht r = math please help...........
Answer:
r = -8.6
Step-by-step explanation:
ooooo IXL, one of my fav programs from my school days
Anyway
Multiply by -3 to get rid of that awful fraction
[tex]-3*2.2=\frac{r+2}{-3} *-3[/tex]
Solve that:
[tex]-6.6=r+2\\aka: r+2=-6.6[/tex]
Subtract 2 from both sides to isolate the r variable:
[tex]r=-8.6[/tex]
And.... We have our answer!
r = -8.6
Does 4f+2(12 f−4)=3(2f−4)−f+3 have one solution, no solution, or infinitely many solutions?
Based on the calculations, this equation 4f + 2(12f − 4) = 3(2f − 4) − f + 3 has one solution, which is equal to -1/23.
What is no solution?In Mathematics, no solution is also referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
This ultimately implies that, an equation would have no solution or zero solution when both sides of the equal sign are not the same and the variables cancel out.
From the information provided, we have the following equation:
4f + 2(12f − 4) = 3(2f − 4) − f + 3
Opening the bracket, we have:
4f + 24f - 8 = 6f - 12 - f + 3
28f - 8 = 5f - 9
By collecting like terms, we have the following:
28f - 5f = -9 + 8
23f = -1
Dividing both sides by 23, we have:
f = -1/23
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For which equation would x = 5 be a solution?
3x+6=21
12-2x = 13
7+ 6 x = 27
4x-7=27
Graph y > -
5x + 5.
4
(I suggest using desmos graphing calculator for the future.)
(0,5) and (4,0) or the one in the left upper corner. Hope this helps.
A surveywas giben to people who awned a cerrain type of car what percent of the people surveyd were completely satisfief with the car?
Using the percentage concept, it is found that 60.29% of the people surveyed were completely satisfied with the car.
A percentage is the number of desired outcomes, multiplied by 100%, and divided by the number of total outcomes.
In this problem, researching in the internet, it is found that:
A total of 1260 + 650 + 180 = 2090 people were surveyed.
Of those, 1260 were completely satisfied.
Hence:
60.29% of the people surveyed were completely satisfied with the car.
The perimeter of an ICU ward, that is rectangular in shape, is 258 feet. The width is 37 feet less than the length. Find the dimensions of this ward.
Find Length(ft) and Width(ft)
The dimensions of the rectangle is 83 feet x 46 feet
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
The perimeter P of the rectangle = 258 feet
Let the length of the rectangle be = L
Let the width of the rectangle be = W
And , The width is 37 feet less than the length. ,
So , W = L - 37
Perimeter P = 2 ( Length + Width )
Substituting the values of L and W in the equation , we get
Perimeter P = 2 ( L + L - 37 )
2 ( L + L - 37 ) = 258
( L + L - 37 ) = 129
2L - 37 = 129
Adding 37 on both sides , we get
2L = 166
Divide by 2 on both sides , we get
Length L of the rectangle = 83 feet
Substituting the value of L in equation ,we get
W = L - 37
Width W of the rectangle = 46 feet
Therefore , Length = 83 feet and Width = 46 feet
Hence , the dimensions of the rectangle is 83 feet x 46 feet
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A company issues 9%, 4-year bonds with a par value of $160,000 on January 1 at a price of $165,386, when the market rate of interest was 8%. The bonds pay interest semiannually. The amount of each semiannual interest payment is:
The amount of each semiannual interest payment is $7200.
Given that,
A company issues 9%, 4-year bonds with a par value of $160,000 on January 1 at a price of $165,386, when the market rate of interest was 8%. The bonds pay interest semiannually.
Simple interest is defined as the percentage of earnings on the lending for a period of time
Here,
Value of a single bond = $160,000
Issue price of bond = $165, 386
Rate of interest = 9%
the market rate of interest = 8%
Interest payment = Semi-annually
Semi-annual interest payment = Value of the single bond × rate of interest/2
= $160,000 × 0.09/2
= $7200
Thus, the amount of each semiannual interest payment is $7200.
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Graph the function with the given domain. Then identify the range of the function.
1) y = -6; domain: x ≥ 5
2) y = -x - 1; domain: -1 ≤ x ≤ 3
The curved part of this figures is a semicircle.
What is the best approximation for the area of this figure?
Responses
28+16.25π units²
18 plus 16.25 pi, units²
14+16.25π units²
14 plus 16.25 pi, units²
14+8.125π units²
14 plus 8.125 pi, units²
28+8.125π units²
28 plus 8.125 pi, units²
Coordinate plane with axes labeled x and y. A closed figure is formed by two segments and a semicircle. A segment extends from negative 4 comma negative 2 to negative 4 comma 2. Another segment extends from negative 4 comma 2 to 3 comma 2. A semicircle extends from 3 comma 2 to negative 4 comma negative 2.
The correct option regarding the area of the figure is given as follows:
14+16.25π units².
How to obtain the area of a figure?The figure, given with no scale at the end of the answer, is composed by:
A semi-circle.A right-triangle.The sides of the right-triangle are given as follows:
7, as 3 - (-4) = 7.4, as 2 - (-2) = 4.The area of a right triangle is given by half the multiplication of the sides, hence:
At = 0.5 x 7 x 4 = 14 units.
The radius of the semicircle is half the hypotenuse of the right triangle, hence, applying the Pythagorean Theorem:
h² = 7² + 4²
h = sqrt(7² + 4²)
r = 0.5sqrt(7² + 4²)
r = 4.03 inches.
The area of a semicircle of radius r is:
As = πr².
Hence:
As = π(4.03)² = 16.25 π.
The total area is obtained as the sum of the areas of each separate part, hence:
A = At + As = 14+16.25π units².
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Answer:
Step-by-step explanation:
14+8.125
C
A caterpillar eats 75 leaves in 5 hours. How many leaves will the caterpillar eat in 8 hours if it continues to eat at the same rate?
The first section of a newspaper has 16 pages. Advertisements take up 3 and 3/8 of the pages. How many pages are not advertisements?
A total of 12 5/8 pages is not meant for advertisement
How to determine the number of pages that are not for adverts?From the question, we have the following parameters
First section = 16 pages
Pages for advertisement = 3 and 3/8 pages
Rewrite the above parameters as
First section = 16 pages
Pages for advertisement = 3 3/8 pages
The number of pages that are not for adverts is then calculated as
Pages not for adverts = First section - Pages for advertisement
Substitute the known values in the above equation
So, we have the following equation
Pages not for adverts = 16 - 3 3/8
Evaluate the difference
Pages not for adverts = 12 5/8
Hence, the number of pages that are not for adverts is 12 5/8 pages
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A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed 70 patients. The sample mean was 1.5 hours with a sample standard deviation of 0.5 hours.
Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)
The distribution that is needed for the problem that we have here is the t distribution.
What is the t distribution?With its bell-shaped structure and heavier tails, the t-distribution, commonly referred to as the Student's t-distribution, is a kind of probability distribution that resembles the normal distribution.
When there are insufficient samples or unknown variances, it is used to estimate population parameters. T-distributions have broader tails than normal distributions because they are more likely to contain extreme values.
We have tn-1
where n = 70
so that we would have
t70 - 1
= t69
Therefore we would have to use the t distribution here.
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What is the greatest common factor (GCF)?
b^5+ 2b^4+ 3b^3+b^2
A. 2b
B. b^2
C. b^3
D. 3b^4
The Greatest Common Factor is [tex]b^{2}[/tex] Option B
What is Greatest Common Factor?The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers
Find the common factors of each term in order to find the greatest common factor (GCF).
The Prime Factors of:
[tex]b^{5}[/tex] = [tex]b^{5}[/tex]
2[tex]b^{4}[/tex] = 2[tex]b^{4}[/tex]
[tex]3b^{3}[/tex] = [tex]3b^{3}[/tex]
[tex]b^{2}[/tex] = [tex]b^{2}[/tex]
From the common factors, the greatest common factors is [tex]b^{2}[/tex]
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help for brainlest????
Answer:
The answer is 55, you can figure this out as each number is increasing by 10
a_n=-5+10n
hope it helps
Complete each ordered pair so that it is a solution of the given linear equation. x +2y=4
The ordered pairs that are solutions to the linear equation x + 2y = 4 are given as follows:
(-3,3.5).(18,-7).How to complete the ordered pairs?The linear function in this problem is defined as follows:
x + 2y = 4.
To complete the ordered pairs, we take the given coordinate and then solve for the missing coordinate .
For the first ordered pair, the given coordinate is of x = -3, hence we have to solve for y when x = -3, thus:
-3 + 2y = 4.
2y = 7.
y = 7/2
y = 3.5.
Hence the ordered pair is:
(-3, 3.5).
For the second ordered pair, the given coordinate is of y = -7, hence we have to solve for x when y = -7, thus:
x + 2y = 4.
x - 14 = 4
x = 18.
Hence the ordered pair is:
(18, -7).
Missing InformationThe ordered pairs that we have to complete are given as follows:
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Write an expression, in terms of h, for the perimeter of this triangle.
Simplify your answer fully.
7
14-6h
3h+3
Answer:
P = 24 - 3h-----------------------------------
It is assumed the sides of the triangle are7, 14 - 6h and 3h + 3Perimeter is the sum of three sidesP = a + b + cP = 7 + 14 - 6h + 3h + 3 = (7 + 14 + 3) + (3h - 6h) = 24 - 3hAnswer:
Perimeter = -3h + 24
Step-by-step explanation:
Forming the expression,
→ 7 + (14 - 6h) + (3h + 3)
Let's simplify the expression,
→ 7 + (14 - 6h) + (3h + 3)
→ 7 + 14 - 6h + 3h + 3
→ (-6h + 3h) + (7 + 14 + 3)
→ -3h + 24
Hence, answer is -3h + 24.
Tammy must choose a number between 61 and 107 that is a multiple of 3,9 and 12. Write all the numbers that she could choose
Answer:
G LCM (least common multiple) of 3, 9, and 12. After doing that, find the number that is between 61 and 107.
Step-by-step explanation:
Least common multiple (lcm) is where g finds out the number that can be divided by all the numbers (3, 9, and 12 in this case) and still come out with a whole number.
PLEASE HURRY I WANT TO FINISH THIS TEST PLEASE ASAP!!
Determine which integer will make the inequality x − 4 < 16 true.
The integers that would make the inequality true is the set of integers less than 20.
Solving Linear inequalitiesFrom the question we are to determine the integer that would make the given inequality true
The given inequality is
x - 4 < 16
To determine the integer that would make the inequality true, we will solve the inequality for the variable x
Solving the inequality
x - 4 < 16
Add 4 to both sides of the inequality
x - 4 + 4 < 16 + 4
x < 20
Hence, the solution to the given inequality is x < 20. All integers less than 20 will make the inequality true.
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The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in cm2/min) is the surface area of the ball increasing when the radius is 6 cm?
The rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.
Surface area of SphereThe surface area of a sphere with radius r is given by4π[tex]r^{2}[/tex]
Given;
S = surface area at time t, and r = radius at time t
radius of a spherical ball is increasing at a rate of 2 cm/min
radius: 6cm
Area of a sphere is A = 4π[tex]r^{2}[/tex]
Step 1: Differentiate area of a spherical ball
A = 4π[tex]r^{2}[/tex]
[tex]\frac{dA}{dt}[/tex] =[tex]\frac{d}{dt}[/tex](4π[tex]r^{2}[/tex])
=4π [tex]\frac{d}{dt}[/tex]([tex]r^{2}[/tex])
=4π2r [tex]\frac{dr}{dt}[/tex]
[tex]\frac{dA}{dt}[/tex] = 8πr
since we have that dr/dt = 2 cm/min. Thus, the radius of the ball is 6cm, we have;
[tex]\frac{dA}{dt}[/tex]= 8π(6)(2) =96π
So, the rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.
Note that measuring area unit is cm2/min
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Josephine invests £3,500 in a bank account which pays annual compound interest of 4.5%. How much money will she have in the bank after: (a) 2 years, (b) 3 years?
Josephine have £3882.9 amount after 2 years and £3994.9 amount after 3 years.
Using the formula of compound interest we can find the amount after t years compounded annually at the r per cent rate.
The formula of compound interest is as follows,
[tex]A=p(1+\frac{r}{100} )^t[/tex]
Where P is the principal value, A is the amount, r is the rate and t is the time.
Here we have a principal value of £3,500 and a rate is 4.5%.
Now, finding the amount after 2 years by putting the values in the formula of compound interest,
[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^2\\\\A=3500(1+0.045 )^2\\A=3500(1.045)^2\\A=3500\times1.092025\\A=3882.0875[/tex]
So, After 2 years Josephine will have £3882.9.
Now, finding the amount after 3 years,
[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^3\\\\A=3500(1+0.045 )^3\\A=3500(1.045)^3\\A=3500\times1.141166125\\A=3994.0814375[/tex]
So, After 3 years Josephine will have £3994.9.
Therefore, After 2 years Josephine will have £3882.9 and after 3 years Josephine will have £3994.9 when 4.5% interest is compounded annually.
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Please help I’ve been stuck on this question for awhile thanks:)
Does anyone know how to do this?
The length of BC is 50 miles (approx).
What is Trigonometry?
Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.
Solution:
In the triangle ABC,
The perpendicular = BC
The Base = AB = 6 miles
by using the trigonometric ratio "tan"
tan (58) = BC / AB
8.33 = BC / 6
49.98 miles = BC
BC = 50 miles (approx)
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