Answer:
[tex]4y = 16-2x\\y = \frac{16}{4} - \frac{2x}{4}\\ y = \frac{-1x}{2}+4\\y = 0.5x+4[/tex]
Given parameters:
Equation of the straight line;
2x + 4y = 16
The slope intercept form of the equation is y = mx + c
Where m is the slope of the line
y and x are the coordinates
c is the intercept
So, the problem is to write the given equation in form of y = mx + c;
2x + 4y = 16
4y = 16 - 2x
Divide through by 2;
[tex]\frac{4y}{2}[/tex] = [tex]\frac{16}{2}[/tex] - [tex]\frac{2x}{2}[/tex]
2y = 8 - x
2y = -x + 8
Then divide by 2 all through;
[tex]\frac{2y}{2}[/tex] = [tex]\frac{-x}{2} + \frac{8}{2}[/tex]
y = [tex]\frac{-x}{2} + 4[/tex]
The equation of the line is y = [tex]\frac{-x}{2} + 4[/tex]
Find the Highest Common Factor of 42 and 90.
Answer:
6
Step-by-step explanation:
Factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factores of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
6 is the greatest common factor.
Answer:
6
Step-by-step explanation:
The common factors of 42 and 90 are 6,3,2,1
Therefore the greatest common factor of 42 and 90 is 6
A circle has the equation x² + y2 = 7
P is the point (-2,13) on the circle x² + y2 = 7
Work out the equation of the tangent to the circle at P.
Answer:
A tangent to a circle at point P with coordinates is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form y = m x + c .
Step-by-step explanation:
Answer:
x=√−y2+7 or x=−√−y2+7
Step-by-step explanation:
Sofia buys a two-gallon bottle of juice for $35.84. What is the unit rate of the cost of the juice per fluid ounce?
Answer:
$/£ 0.14
Step-by-step explanation:
1 gallon = 128 Ounces
2 gallons = 256 ounces
35.84 ÷ 256 = $/£0.14
Answer: $0.14 per fl oz
Step-by-step explanation:
# of fluid oz per gallon = 128
2 gallons = 256 fl oz
$35.84/256= 0.14
Determine whether the sequence is arithmetic, geometric, or neither: 20,17,14,11
==================================================
Explanation:
Add -3 to each term to get the next term. This is the same as subtracting 3 from each term. In this case, the common difference is d = -3.
The first term is a = 20
---------
The nth term formula for the arithmetic sequence is
a(n) = a+d(n-1)
a(n) = 20+(-3)(n-1)
a(n) = 20-3n+3
a(n) = -3n+23
If we plug in n = 1, we would get a(n) = 20. Plug in n = 2 to get a(n) = 17. And so on. This helps confirm we have the correct nth term formula.
Work out the length QR.
Give your answer correct to 3 significant figures.
Total marks: 5
Answer:
The length of QR is 29.9 cm
Step-by-step explanation:
Let us revise the sine and cosine rules
In triangle ABC:
[tex]\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}[/tex] ⇒ sine rule
(AC)² = (AB)² + (BC)² - 2(AB)(BC)cos(∠B) ⇒ cosine rule
Let us use these rules to solve the question
In Δ PQS
∵ [tex]\frac{PS}{sin(Q)}=\frac{QS}{sin(P)}[/tex]
∵ PS = 11.7 cm
∵ m∠P = 95°, m∠Q = 28°
→ Substitute them in the rule above
∴ [tex]\frac{11.7}{sin(28)}=\frac{QS}{sin(95)}[/tex]
→ By using cross multiplication
∴ QS × sin(28) = 11.7 × sin(95)
→ Divide both sides by sin(28) to find QS
∴ QS = 24.82680292 cm
Now let us use the cosine rule to find QR
In Δ QSR
∵ (QR)² = (QS)² + (RS)² - 2(QS)(RS)cos(∠QSR)
∵ RS = 10.2 cm
∵ m∠QSR = 110°
→ Substitute these values in the rule above
∴ (QR)² = (24.82680292)² + (10.2)² - 2(24.82680292)(10.2)cos(110)
∴ (QR)² = 893.631984
→ Take √ for both sides
∴ QR = 29.89367799
→ Round it to 3 significant figures
∴ QR = 29.9 cm
What is the exact length of EC?
A. 4√29/7 Feet
B.√164 Feet
C. 4√5 Feet
D. 2√41 Feet
Answer:
C. [tex]4\sqrt{5}[/tex] feetStep-by-step explanation:
We have similar triangles:
ΔADC ~ ΔBECFind segment BC using similarity and ratios:
AD/ BE = AC / BC28 / 8 = (10 + BC)/ BC28BC = 8(10 + BC)28BC = 8BC + 8020BC = 80BC = 4Find EC using Pythagorean:
[tex]EC = \sqrt{BE^2+BC^2}=\sqrt{8^2+4^2}=\sqrt{64+16}=\sqrt{80}=4\sqrt{5}[/tex]Correct choice is C
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.
x2-30x+
Answer:
225
Step-by-step explanation:
a[tex]x^{2}[/tex] - bx + c
[tex](\frac{b}{2}) ^{2}[/tex]
[tex](\frac{-30}{2}) ^{2}[/tex]
[tex](-15)^{2} \\[/tex]
225
[tex](x-15)^{2}[/tex] = [tex]x^{2}[/tex] - 30x + 225
If x+y=8 , 1/x+1/y=1/2 then xy=?
Answer:
xy = 16
Step-by-step explanation:
[tex]\frac{1}{x}[/tex] + [tex]\frac{1}{y}[/tex] = [tex]\frac{1}{2}[/tex] ( multiply through by 2xy to clear the fractions )
2y + 2x = xy ← factor out 2 from each term on the left side
2(y + x) = xy
substitute x + y = 8 into the left side
2(8) = xy , that is
xy = 16
Drake’s monthly outlay include a $70 phone bill and a $120 car assuming he makes $400 a month, how much does he have to spend after paying his bills?
The solution is, $210 does he have to spend after paying his bills.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
given that,
Drake’s monthly outlay include a $70 phone bill and a $120 car assuming he makes $400 a month,
i.e. we get,
Drake’s monthly outlay include a $70 phone bill and a $120 car.
so, total spend = $ 120 + 70
= $190
now, we have to find how much does he have to spend after paying his bills.
so, we have to subtract 190 from 400
i.e. 400 - 190
=210
Hence, $210 does he have to spend after paying his bills.
To learn more on subtraction click:
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#SPJ2
Need help with question 10- Tysm!
Answer:
A=½bh
56=8a(½)
multiply by reciprocal both sides
112=8a
divide
14=a
Find the equation of the line shown
Answer:
y=x+1
Step-by-step explanation:
The slope of the equation is 1, you can try the rise over run method or picking 2 points and subtracting them for example 2,3 and 3,4
2,3-3-4=1,1. The y-intercept is 1 because that is the point where the line crosses the y axis.
Answer:
Slope intercept form:
y = mx + b
Where 'y' is the independent variable and 'x' is the dependent variable.
'm' represents the slope(rise/run), and 'b' represents the y-intercept(where the line meets the y-axis).
If we look at this graph, we can see the line meets the y-axis at 1. So 1, will be our y - intercept.
We can also see, that from the point 1, it rises 1 and goes over 1. So 1, will be our slope as well.
To double check this, we select two fixed points on this graph and subtract the y-coordinates from each other and divide the result of that by the x-coordinates subtracted from each other.
y2(second y-coordinate) - y1(first y-coordinate)
_____________________________________
x2(second x-coordinate) - x1(first x-coordinate)
We pick the two points to be, (1,2) and (2,3).
3 - 2 1
______ = _______, which is equal to 1, so 1 is the slope.
2 - 1 1
Now we insert these values into our slope intercept form equation:-
y = mx + b
y = 1x + 1 or y = x + 1.
Where 1 is the slope, and the y-intercept is 1.
Pls help will give brainlist and 100 points.
[tex]\\ \tt\hookrightarrow (x+5)(x+8)[/tex]
[tex]\\ \tt\hookrightarrow x(x+8)+5(x+8)[/tex]
[tex]\\ \tt\hookrightarrow x^2+8x+5x+40[/tex]
[tex]\\ \tt\hookrightarrow x^2+13x+40[/tex]
Done!
James studied for his test. He started studying at 3:20 p.m. and studied for 2 hours and 15 minutes. What time did he finished studying?
18 POINTS!
Hey there!
Started at 3:20 and studied for 2 hours and 15 minutes
=> [tex]3:20 \\ 2:15 \\ \overline{5:35} \\ \overline{ } [/tex]
Therefore, He finished at 5:35
find √100 please i need help
Answer:
10
Step-by-step explanation:
as you want to find the square root of 100, by using a calculator you will find out that it is 10, also in other way you can check whether it is true by multiply 10 with 10, which you will get 100. in other way, square root of 100 means what value times with what value will get 100
Hey there!
First of all, what is this "√" sign?
It means "square root"
Wow, numbers have square roots? Yes.
The square root of a number is the opposite of squaring a number.
Squaring a number simply means multiplying it times itself.
So taking the square root of a number is the opposite of squaring a number.
So, we have
[tex]\bold{\sqrt{100} }[/tex]
What is the square root of 100? in other words, what number times itself equals 100?
That's right, 10.
Hence, the answer is:
[tex]\boxed{\boxed{\bold{10}}}[/tex]
Hope everything is clear.
Let me know if you have any other questions; if you do, please comment.
#LearningDoesn'tEnd
[tex]\rule{200}{2}[/tex]
A wedding tent is built in the shape of a right rectangular prism topped with a
rectangular pyramid. The dimensions of the prism are 21 ft by 27 ft by 8 ft,
and the height of the pyramid is 2 ft. Find the total volume of the tent. Round
your answer to the nearest tenth if necessary.
Based on the calculations, the total volume of this wedding tent is equal to 4,914 [tex]ft^3[/tex]
Given the following data:
Dimensions of prism (LWH) = 21 ft x 27 ft x 8 ft.Height of pyramid = 2 ft.How to calculate the total volume of the tent.First of all, we would determine the volume of the right rectangular prism by using this formula:
[tex]V=LWH\\\\V=21 \times 27 \times 8\\\\V=4536\;ft^3[/tex]
Also, we would determine the volume of the pyramid by using this formula:
[tex]V=\frac{1}{3} BH\\\\V=\frac{1}{3}\times (21\times 27)\times 2\\\\V=378\;ft^3[/tex]
For the total volume:
Total volume = [tex]4536+378[/tex]
Total volume = 4,914 [tex]ft^3[/tex]
Read more on rectangular prism here: brainly.com/question/3867601
Please answer and say what a perfect root is pls i didnt get time to study and this is for 15 points
Answer:
81 is a perfect square
18 isn't a perfect square
50 isn't a perfect square
32 isn't a perfect square
Step-by-step explanation:
Numbers whose square roots are whole numbers, or more accurately positive integers are called perfect root
Example 7×7=49
What is the value of the expression 2^2 + 8^2 ÷ 2^2?
1 point)
8
10
17
20
Answer:
Fourth option
Step-by-step explanation:
Given the following question:
[tex]2^2+8^2\div2^2[/tex]
To find the answer we need to convert the exponents into integers and then solve using PEMDAS.
[tex]2^2+8^2\div2^2[/tex]
[tex]2^2=2\times2=4[/tex]
[tex]8^2=8\times8=64[/tex]
[tex]2^2=2\times2=4[/tex]
[tex]4+64\div4[/tex]
[tex]64\div4=16[/tex]
[tex]4+16[/tex]
[tex]4+16=20[/tex]
[tex]=20[/tex]
Your answer is "20" or the fourth option.
Hope this helps.
(Maths)
Line R has the equation y = 4x + 7
Line P is parallel to line R and intersects the y-axis at (0,-5)
Write down the equation of line P in thee form y=mx+c
Answer:
y = 4x + -5
Step-by-step explanation:
Answer:
[tex]y=4x-5[/tex]
Step-by-step explanation:
parallel lines have the same gradient so line P's gradient would also be 4
line P's equation is [tex]y=4x+c[/tex] but we don't know the c variable yet, so we just plug in the coordinate values
[tex]-5=4(0)+c[/tex]
[tex]-5=c[/tex]
so line P's equation is [tex]y=4x-5[/tex]
A bag contains 1 blue, 2 green, and 2 red marbles. You choose a marble with one hand and then a second marble with the other hand. What is the probability that you will first choose a red marble followed by a green marble?
The probability that you will first choose a red marble followed by a green marble is 20%.
ProbabilitiesGiven that a bag contains 1 blue, 2 green, and 2 red marbles, and you choose a marble with one hand and then a second marble with the other hand, to determine what is the probability that you will first choose a red marble followed by to green marble the following calculation must be made:
1 + 2 + 2 = 52/5 x 2/4 = X0.4 x 0.5 = X0.2 =X0.2 x 100 = 20Therefore, the probability that you will first choose a red marble followed by a green marble is 20%.
Learn more about probability in https://brainly.com/question/26677483
The probability of choosing a red marble is 2/5 while the probability of choosing a green marble after a red marble is 1/2
Data;
blue = 1green = 2red = 2Probability without replacementTo solve this problem, we have to do probability without replacement.
The total number of marbles in the bag is
[tex]1 + 2 + 2 = 5[/tex]
The probability of choosing a red marble is
Number of read marbles = 2
probability of choosing a red marble is
[tex]P = \frac{2}{5}[/tex]
The probability of choosing a green marble after a red marble is
[tex]P = \frac{2}{4} =\frac{1}{2}[/tex]
The probability of choosing a red marble is 2/5 while the probability of choosing a green marble after a red marble is 1/2
Learn more on probability here;
https://brainly.com/question/251701
Elizabeth has 5/6kg of beads. IF she shares the beads between 4 friends, how much kg does each friend receive.
Answer:
5/24 kg
Step-by-step explanation:
5/6 ÷ 4/1 (keep-change-flip)
5/6 x 1/4 = 5/24
Which is a better deal?
75% off of a brand name mp3 player that costs $199
OR an off-brand mp3 player for $44.99
Answer:
Off-brand mp3 for $44.99
Step-by-step explanation:
Given;
75% off of a brand name mp3 player that costs $199 or an off-brand mp3 player for $44.99
Note;
off = discount = decrease
Solve;
Starting with brand name mp3
$199 x 75% = 149.25
199 - 149.25= 49.75
Now with off brand mp3
$44.99 x 75% = 33.7425
Round 33.7425 = 33.74
$44.99 - 33.74 = 11.25
49.75 > 11.25
Hence, we can see that off-brand mp3 player is a better deal.
~Learn with Lenvy~
The volume of a cylinder is approximately 942 cubic inches. The height of the cylinder is 12 inches. Which is the best approximation for the radius of the cylinder? 4 inches, 6 inches, 7 inches, 5 inches
Answer: 5 inches
Step-by-step explanation:
The volume of a cylinder is equal to pi*radius^2*height.
We can replace the height with 12 inches and the volume with 942 cubic inches.
Therefore, 942 in^3 = pi*radius^2*12 inches
We can divide both sides by 12:
pi*radius^2 = 78.5 inches^2
We can divide both sides by pi:
Radius^2 = About 24.99 inches^2
We can square both sides:
Radius approximately equals 5 inches.
In the image below, find the value of x
, m∠7
, and m∠8
.
m∠7=5x+5
m∠8=x−5
Answer:
Step-by-step explanation:
<7 + <8 = 180 [They are supplementary.]
5x + 5 + x - 5 = 180
6x = 180
x = 180/6
x = 30
==================
m<7 = 5x + 5 = 5*30 + 5 = 150+5 = 155
m<8 = x - 5 = 30 - 5 = 25
What common fraction must be taken from 5/6 to equal 1/3
Answer:
1/2
Step-by-step explanation:
[tex] \frac{5}{6} - x = \frac{1}{3} [/tex]
[tex] \frac{5}{6} - x = \frac{2}{6} [/tex]
[tex]x = \frac{3}{6} = \frac{1}{2} [/tex]
Find find the area of the triangle below
Answer:
the answer is: 70
Step-by-step explanation:
[tex]s \: = \: \frac{ah}{2} [/tex]
[tex]s \: = \: \frac{70 \: \times \: 20}{2} = \: 70[/tex]
What is an equation of the line that passes through the points (-6,-4) and
(-4,0)?
Answer:
y = 2x + 8
Step-by-step explanation:
the equation of a line in slope-intercept form is.
y = mx+b
where m is the slope and b the y-intercept
to calculate m use the gradient formula
m = (y2−y1 ) / (x2−x1)
let (x1,y1)=(-6,-4) and (x2,y2)=(-4,0)
m = (0 - (-4)) / (-4 - (-6) = 2
y = 2x+b←is the partial equation
to find b substitute either of the 2 given points
into the partial equation
using (-6, -4) then
-4 = -12+b⇒b=8
y = 2x + 8←is the equation of line
In 2015,there were about 22 million teenagers (aged 13-17) in the United States. They each sent an average of 900 text messages per month. About how many text messages did all of the teenagers in the United States send each month? Express your answer using scientific notation
The amount of text messages sent by teenagers in the United States in 2015 is about 1.98 x [tex]10^{10}[/tex]
What is scientific notation?Scientific notation is used in expressing large numbers in smaller numbers. It is used to transform large numbers into smaller number. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
2.2 x 10^7 + 9 x 10^2 = 1.98 x 10^10
To learn more about scientific notation, please check: https://brainly.com/question/25334755
ASAP PLS HW EXPLANATION NEEDED
REMEBER IT SAYS SELECT ALL
Answer:
A and C are stories that can be represented by the tape diagram.
what is the 63 term in the sequence 2,12,22,32,....
Please mark brainliest this took a while to make!
Answer:
622
Counting the terms already shown, we would need 59 more. Since each term adds ten, let's make each term 10 added to the previous.
2,12,22,32,42,52,62,72,82,92,102,112,122,132,142,152,162,172,182,192,202,212,222,232,242,252,262,272,282,292,302,312,322,332,342,352,362,372,382, 392,402,412,422,432,442,452,462,472,482,492,502,512,522,532,542,552, 562,572,582,592,602,612,622
Pedro jogs 1.45 kilometers on Monday. he jogs 0.5 kilometer more on Tuesday than on Monday. how far does Pedro jog during both days?
Answer:
3.4 kilometers on both days
Step-by-step explanation:
[tex]1.45+0.5=1.95[/tex]
[tex]1.45+1.95=3.4[/tex]