The equation of the line that has a slope of -4 and goes through -1,6 is 4x-y+2 = 0
What is equation of the line?In general, a straight line has the equation y = mx + c, where m denotes the gradient and y = c denotes the point at which the line intersects the y-axis. The y-axis intercept is denoted by the value c. A straight line with a gradient of m and an intercept of c on the y-axis has the equation y = mx + c. Finding the slope and y-intercept will allow you to write the equation of a graphed line in y-intercept (y=mx+b) form. Slope is defined as the ratio of y-to-x changes. Choose two points on the line, and then create a sloping triangle joining them.
The equation of a straight line that passes through a point [x1 , y1} and having a slope ‘m’ is given by (y - y1) = m (x - x1)
Given m = 4 and point ( 1,6), then the equation of the line is
(y-6) = 4 (x-1) i.e, y - 6 = 4x - 4
i.e, 4x -y -4+6 =0 i.e, 4x - y = - 2 or 4x-y+2 = 0
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Please simply 24/64
2/6
3/8
1/3
6/16
A town has a population of 5000 and grows at 5% every year. To the nearest tenth of a year, how long will it be until the population will reach 8100?
To the nearest tenth of a year, it will be approximately 27.4 years for the population to reach 8100.
What is the growth rate?
Growth rates are used to express the annual change in a variable as a percentage. A positive growth rate indicates a variable is increasing over time; a negative growth rate indicates that it is decreasing.
To find out how long it will take for the town's population to reach 8100, we can use the formula:
time = (ln(8100/5000)) / ln(1 + growth rate)
where growth rate is 0.05 (5%) and ln is the natural logarithm.
Plugging in the numbers we get:
time = (ln(8100/5000)) / ln(1 + 0.05) = (ln(1.62)) / ln(1.05)
Hence, To the nearest tenth of a year, it will be approximately 27.4 years for the population to reach 8100.
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Answer:
The correct answer would be 9.9.
Step-by-step explanation:
Layla ate 3/8 of the pie her mother made. What part of the pie Layla not eat
-58.8 ÷ -245 + (-3.5 x 2) ^3
Answer:
=−42.875x6+0.24
Step-by-step explanation:
−58.8
−245
+(−3.5x2)3
=0.24+−42.875x6
scott wants to buy a new tablet that costs 440 after taxes. he earns 11.50 per hours each week. of scott spends 100 each week on food and saves the rest for the tablet how long would it be for him to save money for the tablet
He can buy the tablet though it costs 440 after taxes just within 2 days by the given information.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables, constants.
Given,
scott wants to buy a new tablet that costs 440 after taxes. he earns 11.50 per hours each week. of scott spends 100 each week on food
and saves the rest for the tablet.
per hour he earns 11.50 so per day could be = 11.50*24
= 276.
So, per day he earns 276.
So, for 2 days = 276*2
= 552
So, let us suppose in this only he spent 100 for food
so,
remaining amount could be 552-100
= 452
he can buy the tablet though it costs 440 after taxes .
Hence, he can buy the tablet though it costs 440 after taxes just within 2 days by the given information.
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Find (g ○ f )(x ) where `f(x)=x2+8,g(x)=5x-2.
Answer:
(g ○ f)(x) = 5x² + 38
Step-by-step explanation:
to find (g ○ f)(x) substitute x = f(x) into g(x) , that is
g(f(x)
= g(x² + 8)
= 5(x² + 8) - 2
= 5x² + 40 - 2
= 5x² + 38
What is the value of the expression below?
14+2+3(4)-(6-1-3)
1.10/2
2.15-12
3.30-1/
4.36-1/
THe value of the expression using BODMAS rule is 26
What is BODMAS rule ?The abbreviation BODMAS, which stands for "Brackets, Order of powers or roots, Division, and Multiplication," is followed by the BODMAS rule. A stands for addition and S for subtraction. According to the BODMAS rule, multi-step mathematical statements must be solved in the BODMAS order from left to right.
The order of operations, or BODMAS, is a method for carrying out operations in an arithmetic statement. Math is all about logic, and there are several established laws that help us with our calculations. BODMAS is one of the established rules for consolidating multiple operator expressions.
An expression or equation in mathematics has two parts:
NumbersOperatorsA character known as an operator joins two integers to form an expression or equation. The four most often used operators in mathematics are addition (+), subtraction (-), multiplication (*), and division (*/*). Finding the solution to mathematical statements or equations with just one operator is usually rather easy.
The expression is 14 + 2 + 3(4) - (6-1-3) = 14 + 2 + 12 - 2 = 26
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The Two-Steppers numbered 10 more than 5 times the number of waltzers. Also there were 10 times as many Two-steppers as waltzers. How many of each were there?
Answer: I think it is 1,200
Step-by-step explanation: search it up
Given f(x)= 4x^2 - 4 + 1 and g(x)= 2x-1, which of the following are expression(s) for f•g? Select all that apply.
The value for the expression, (f * g)(x) is calculated as: C. 8x³ - 12x² - 6x -1
How to Evaluate the Expressions of Functions?
We are given the following functions,
f(x) = 4x² – 4x + 1 and g(x) = 2x – 1.
To find the value of the expression, (f * g)(x), it means we have to multiply the functions together. See the steps explained below.
(f * g)(x) = f(x) * g(x)
Plug in the values:
(f * g)(x) = f(x) * g(x) = (4x² – 4x + 1)(2x – 1)
(f * g)(x) = 4x²(2x – 1) - 4x(2x – 1) + 1(2x – 1)
Apply the distribution property of equality:
(f * g)(x) = 8x³ – 4x² - 8x² + 4x + 2x – 1
Combine like terms:
(f * g)(x) = 8x³ - 12x² - 6x - 1
Therefore, the answer is: C. 8x³ - 12x² - 6x - 1.
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←
Find a if XZ = 125,
XY = 3a and YZ = 2a.
Y is 275.Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation.
How can I locate expressions that are equivalent?Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation. The x-term is typically put before constants when arranging the terms in the same sequence. The two phrases are equal if each of the terms in both of them is the same.
Explanation:
x 2 + xy+xz=135; y 2 + yz+ xy=351; z 2 + xz+ yz=243; (iii)
When I (ii), and (iii) are added together, we obtain x 2 + y 2 + z 2 + 2(xy+yz+xz) = 729, which converts to (x+y+z) 2 = 27 2.
x+y+z=27
........
(iv)
According to equation I x 2 + x y + x z = 135 => x(x+y+z) = 135 => x27=135 => x=5
In equation (ii), we have y 2 + y z + x y = 351, which leads to y (x+y+z) = 351.
y×27=351 \s=>
y=13
Once more, we obtain the following from equation (iii): z 2 + x z + y z = 243; z (x + y + z) = 243; z 27 = 243.
z=9 \sx \s2 \s +y \s2 \s +z \s2 \s =5
2 \s +13 \s2 \s +9 \s2 \s =275.
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What is the sum of 11/12 and 11/12 explain for a 4th grader to understand
The sum of the two fractions 11/12 + 11/12 = 11/6
How to add the two fractions?We want to sum the two fractions:
11/12 + 11/12
Remember that always that we add fractions with the same denominator (like in this case) we can directly add the numerators, then in this case the sum will be:
11/12 + 11/12 = (11 + 11)/12 = 22/12
Now we can simplify that fraction by dividing both numeartor and denominator by 2, we will get:
22/2 = 11
12/2 = 6
So we can rewrite the fraction as:
11/6
That is the outcome.
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A bag of Halloween candy contains 4 Snickers, 3 Milky Ways and 5 Kit Kat bars. You reach into the bag, grab a bar and eat it. You reach into the bag, grab a second bar and eat it too. What is the probability of getting a Kit Kat and then a Milky Way?
The probability of getting a Kit Kat and then a Milky Way candy bars is the fraction 5/44
Probability of an event without replacementThe probability of an event without replacement implies that once an item is drawn, then we do not replace it back to the sample space before drawing another item.
total number of candy bars = 12
probability of first getting a Kit Kat candy bar = 5/12
probability of then getting a Milky Way candy bar = 3/11
probability of getting a Kit Kat and then a Milky Way candy bars = 5/12 × 3/11
probability of getting a Kit Kat and then a Milky Way candy bars = 5/44
Therefore, the probability of getting a Kit Kat and then a Milky Way candy bars is the fraction 5/44.
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A diver starts at a depth of 4m below sea level. After half an hour she is Fives Times as deep what is her depth
Answer:
Step-by-step explanation:
20 m i think
What process is shown in the diagram below?
685
E and Emilis Qytapwap and Emera
While Waste Whatsite
MCHOMB
978
A. Use of
restriction
enzymes
electrophoresis
C. Polymerase
chain
reaction
Specifically cutting DNA at the restriction site to create sticky ends, EcoRI is a type II restriction enzyme in nanometer .
what is nanometers ?The International System of Units defines a nanometer, also referred to as a nanometer, as being one billionth of a metre and one thousandth of a picometre. A nanometer is denoted by the digits 1 109 m and 1/1000000000 meters in scientific notation. In the International System of Units, the prefix "nano" denotes a billionth, or 10-9. One billionth of a meter is the size of the metric length unit known as a nanometer (0.000000001 m). It is a short unit of length, denoted by the letter n.
given
On an agarose gel stained with ethidium bromide, the digested DNA may be seen and compared using molecular size ladders.
The ligation reaction becomes more effective as a result. EcoRI is a restriction endonuclease enzyme that was identified from the E. coli species (pronounce "eco R one").
It belongs to the restriction modification system and is a restriction enzyme that breaks down DNA double helices into fragments at particular locations.
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Colleen's family is moving to a new home overseas. They will send their car two thousand miles across the ocean in a shipping container. Their shipping container is twenty feet long, eight feet wide, and eight feet tall. What is the volume of the shipping container?
Answer: The volume of a rectangular container is given by the formula:
Volume = length * width * height
In this case, the length of the container is 20 feet, the width is 8 feet, and the height is 8 feet.
So the volume of the shipping container can be calculated as:
Volume = 2088 = 1,360 cubic feet
So, the volume of the shipping container is 1,360 cubic feet
Step-by-step explanation:
Sheena needs 1 3/4 cups of sugar to make pancakes. She already has 5/8 cups of sugar. How much more sugar does she need?
Answer: 9/8
Step-by-step explanation:
Which arrangement shows 26/4, 6.45, 6 2/5, and 50/8 in order from least to greatest?
A. 50/8, 6 2/5, 26/4, 6.45
B. 6 2/5, 50/8, 6.45, 26/4
C. 50/8, 6 2/5, 6.45, 26/4
D. 26/4, 50/8, 6 2/5, 6.45
20 points.
The arrangement of 26/4, 6.45, 6 2/5, and 50/8 in order from least to greatest is C. 50/8, 6 2/5, 6.45, 26/4.
How can the order be determined?The concept that will be used here is ordering of numbers using < signs.
To arrange the shows, we can convert 26/4, 6.45, 6 2/5, and 50/8 to decimal so this will help us to determine the order.
26/4=6.50
6.45=6.45
6 2/5=32/5 = 6.40
50/8 =6.25
Then 6.25<6.40 <6.45 <6.50 and this implies that the order that the arrangement follows is 50/8, 6 2/5, 6.45, 26/4
Therefore, option C is correct.
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Given the following graph a. Evaluate f (1). f(1) = f b. Solve for f(x) = 1. If there is more than one solution, enter the solutions separated by semicolons (e.g. 2; 4; 6). x
For f(x) = 1 the value of x is 0, -6, and the value of the function at x= 4 or f(4) is -3.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, a function f(x) in the graph
f(x) = y
F(X) represents the function value at various values of x
From graph,
f(4) = -3
Because at x = 4, y = -3
at f(x) = 1
since f(x) = y
y = 1
satisfying at two values of x that are -6, 0
Therefore, For f(x) = 1 the value of x is 0, -6 and the value of f(4) is -3.
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Complete question:
find the equation of tangent and normal to the surface z^2=4(1+x^2+y^2)at (2,2 ,6)
Answer:We have,
f(x,y,z)=2x
2
+y
2
+2z=3
∂x
∂f
=4x,
∂x
∂f
=2y,
∂x
∂f
=2z
Step-by-step explanation:
good luck :}
According to the American Academy of Cosmetic Dentistry, 75% of adults believe that an unattractive smile hurts career success. Suppose that 25 adults are randomly selected. What is the probability that more than 22 of them would agree with the claim?
97.03% probability that 15 or more of them would agree with the claim.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
P(X = x) = [tex]C_{n,x} p^x (1-p)^{n-x[/tex]
where [tex]C _{n,x[/tex] = n! / r! (n-r)!
And p is the probability of X happening.
75% of adults believe that an unattractive smile hurts career success.
p = 0.75
and n = 75
Now, the probability that 15 or more of them would agree with the claim
P(X≥ 15) = 1 - P(X< 15)
So, P(X< 15) = P(X=0) + P(X=1) + P(X=2) + ..........................P(X=14)
and, P (X = 14) = [tex]C_{25, 14} (0.75)^{14} (0.25)^{11[/tex] = 0.0189
P (X = 13) = [tex]C_{25, 13} (0.75)^{13} (0.25)^{12[/tex] = 0.0074
P (X = 12) = [tex]C_{25, 12} (0.75)^{12} (0.25)^{13[/tex] = 0.0025
P (X = 11) = [tex]C_{25, 11} (0.75)^{11} (0.25)^{14[/tex] = 0.0007
P (X = 10) = [tex]C_{25, 10} (0.75)^{10} (0.25)^{15[/tex] = 0.0002
P (X = 9) = [tex]C_{25, 9} (0.75)^{9} (0.25)^{16[/tex] = 0
Then, P(X< 15)
= P(X=0) + P(X=1) + P(X=2) + ..........................P(X=14)
= 0.0002+0.0007+0.0025+0.0074+0.0189
= 0.0297
and, P(X≥ 15) = 1 - P(X< 15)
= 1- 0.0297
= 0.9703.
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ryann has 80$ to spend on gifts. She already decided to use $25 for a scarf for her grandmother. She wants to spend the reaming money to purchase gifts for her four freinds. She will spend the same amount of money for each friend's gift. What is the most she can spend on each friend?
Answer:
Okay so since she has 80 dollars, and already spent 25, then she would have 55 dollars remaining.
Now that she has 55 dollars, she will divide it up evenly between her 4 friends.
55/4 = 13.75
The most that she would be able to give them is $13.75
Step-by-step explanation:
Hope it helps! =D
Today only, a table is being sold for $237.80. This is 29% of its regular price. What was the price yesterday?
Answer:300
Step-by-step explanation:
Which is longer 92.1 or 0.33
Answer:
92.1
Step-by-step explanation:
0.33 is smaller then 92.1, so 92.1 would be longer.
(I was the one who gave it a 1 star since I was fooling around, lol)
Zach solves the system below and finds the solution (8, -7).
x + y = -15
x + y = -1
Use a graph to complete the explanation for whether Zach's solution is reasonable.
<------------> x + y = -15
< -----------> = -1
The graph shows that the of the solution , so Zach's solution reasonable.
If 1% of a number equals 5, find 2% of that number.
If 1% of a number equals 5, find 2% of that number is 2
What are algebraic expressions?Algebraic expressions are described as expressions composed of variables, constants, factors, coefficients and terms.
Arithmetic operations also make up these expressions, they are;
DivisionBracketAdditionParenthesesMultiplicationSubtractionAlso, fractions are described as part of a whole element, number or variable
From the information given, we have that;
1% of a number is 5
Let the number be x
1/2x = 5
Make 'x' the subject
x = 10
Substitute the value
2/10 of x
2/10 × 10
2
Thus, the value is 2
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The ratio of 3 red marbles to every 2 blue marbles
Answer:
yes
Step-by-step explanation:
Gabe goes to the mall. If d is the number of items he bought, the expression 13.09 d plus 28 gives the amount he spent in dollars at one store. Then he spent 22 dollars at another store. Find the expression which represents the amount Gabe spent at the mall. Then estimate how much Gabe spent if he bought 4 items
Estimate the amount that Gabe spent if he bought 4 items will be $102.36.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Gabe goes to the mall. If d is the number of items he bought, the expression 13.09 d plus 28 gives the amount he spent in dollars at one store. Then he spent 22 dollars at another store.
Then the equation that represents the total amount is given as,
T = 13.09d + 28 + 22
T = 13.09d + 50
Then estimate the amount that Gabe spent if he bought 4 items will be given as,
T = 13.09(4) + 50
T = 52.36 + 50
T = $102.36
Estimate the amount that Gabe spent if he bought 4 items will be $102.36.
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find the value of help
Please help
Answer:
[tex]x=29^{\circ}[/tex]
Step-by-step explanation:
Please refer to the picture attached as I labeled the angles.
Given
[tex]\angle{B}=90^{\circ}[/tex]
[tex]\angle{ADB}=58^{\circ}[/tex]
[tex]AD=CD[/tex]
[tex]\angle{ACD}=\angle{CAD}[/tex] which also equals x in your picture.
We need to use the Exterior Angle Property to evaluate x.
This property states that the exterior angle equals sum of two interior opposite angles.
[tex]\angle{ACD}+\angle{CAD}=58^{\circ}[/tex]
Substitute x for [tex]\angle{ACD}[/tex] and [tex]\angle{CAD}[/tex].
[tex]x+x=58^{\circ}[/tex]
Add x and x.
[tex]2x=58^{\circ}[/tex]
[tex]x=29^{\circ}[/tex]
Answer:
The angle is 32
Step-by-step explanation:
The formula for the sum of interior angles is [tex](n-2)180[/tex]
We have a triangle inside a triangle.
A triangle has 3 sides.
[tex](n-2)180\\(3-2)180\\1(180)\\180[/tex]
The picture shows us an angle of 90 and 58.
All 3 angles must add up to 180.
[tex]180-90-58[/tex]
[tex]x=32[/tex]
NO LINKS!!
Please help me with these proofs. Part 1
Given:
C is the midpoint of AE,∠BCA ≅ ∠DCE,∠A ≅ ∠EWe have two pairs of congruent angles and the included sides are congruent. It gives us ASA congruence. AB ≅ DE as corresponding parts of congruent triangles.
Statement Reason
C is the midpoint of AE Given∠BCA ≅ ∠DCE Given∠A ≅ ∠E GivenAC ≅ EC Definition of a midpointΔABC ≅ ΔEDC ASA congruence AB ≅ DE CPCTCProvedProblem 8Given:
AH bisects ∠BHT,AH ⊥ BTWe have two right triangles with common leg and the other pair of legs are congruent as bisected segment. We get SAS congruence with two sides and included right angle.
Statement Reason
AH bisects ∠BHT GivenAH ⊥ BT Given∠BAH ≅ ∠TAH = 90° Definition of perpendicularAH ≅ AH Reflexive property (common side)BA ≅ TA Definition of segment bisectorΔBAH ≅ ΔTAH SAS congruenceProvedProblem 10Given:
AB ⊥ AC,CD ⊥ BD,AC ≅ BDΔABC and ΔCDB are right triangles with common hypotenuse and congruent pair of legs. It gives us HL congruence and it proves the corresponding angles are congruent.
Statement Reason
AB ⊥ AC GivenCD ⊥ BD GivenAC ≅ BD Given∠A & ∠D are right angles Definition of perpendicularBC ≅ BC Reflexive property (common side)ΔABC ≅ ΔDCB HL congruence∠ABC ≅ ∠BCD CPCTCProvedTriangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle T′R′W′. Which ordered pair best represents the location of point R′?
An ordered pair which best represents the location of point R′ include the following: B. (−3n, −5n).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of the preimage (Triangle TRW) by using a scale factor of n centered at the origin as follows:
Ordered pair T (-3, 5) → Ordered pair T' (-3 × n, 5 × n) = Ordered pair T' (-3n, 5n).
Ordered pair R (-3, -5) → Ordered pair R' (-3 × n, -5 × n) = Ordered pair R' (-3n, -5n).
Ordered pair W (4, -5) → Ordered pair W' (4 × n, -5 × n) = Ordered pair W' (4n, -5n).
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Complete Question:
Triangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle T'R'W'. Which ordered pair best represents the location of point R′?
answer choices
(-3/n, -5/n)
(−3n, −5n)
(−3+n,−5+n)
(−3−n,−5−n)