The correct equation of the new line parallel to y = 3x + 2 and passing through (1, 6) is y = 3x + 3.
Explanation:To find the equation of the line that is parallel to the given line y = 3x + 2 and passes through the point (1, 6), we first need to acknowledge that parallel lines have the same slope.
Therefore, the slope of the new line will also be 3. We can use the point-slope form of the equation y - y1 = m(x - x1) to find the equation. Substituting the given point into the equation, we get y - 6 = 3(x - 1).
Simplifying the equation, we find y = 3x + 3. So, the equation of the line that is parallel to the original line and passes through the given point is y = 3x + 3.
What math property is this 19(24)=19(20)+19(4)
Answer:
Distributive Property
Step-by-step explanation:
19(24)=19(20)+19(4)
456 = 380 + 76
456 = 456
Hope this helps
-Amelia
Water tower. Model depth 32cm actual depth is ?m
The question involves converting the model depth from centimeters to meters, which typically requires dividing by 100. However, without a specific scale or additional detail, the direct conversion of 32cm would be 0.32 meters.
Explanation:The student's question is about converting the depth of a model water tower, provided in centimeters, to its actual depth in meters without giving a specific depth in the question. This concept usually involves understanding the scale of models and how to apply proportional reasoning to determine actual sizes. However, without a specific scale or the actual depth given in the question, we can't calculate the actual depth.
Generally, to convert from centimeters to meters directly, we divide the length in centimeters by 100, because 1 meter equals 100 centimeters. For example, if a model tower's depth is 32cm, to find this depth in meters, you would divide 32 by 100, which equals 0.32 meters.
412 Divided by four show your work
Answer:
103
Step-by-step explanation:
You start with long division 4 goes into 4 1 time and then 0 cause you have nothing else drop the 12 and then 4 goes into 12 3 times 103
Answer:
103
Step-by-step explanation:
If you solve it using partial quotients, it would be eaisier to demonstrate than using another method like standard division.
Hope this helps!
-Coconut;)
(-6x3-4x2-8)+(x3-x2-9x+4) add together and simply
Answer:
-5x³ -5x² -9x - 4
Step-by-step explanation:
(-6x³-4x²-8)+(x³-x²-9x+4)
Add the like terms.
-6x³ and x³ are like terms. -6x³ + x³ = -5x³
-4x² and -x² are like terms. -4x² - x² = -5x²
-8 and 4 are like terms. -8 + 4 = -4
-6x³-4x²-8 +x³-x²-9x+4 = -5x³ -5x² -9x - 4
Solving a right triangle ‼️ Can someone help me find A,a and c❓ (Round to the nearest tenth)
Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the given angles from 180 for A
A = 180° - (90 + 48)° = 180° - 138° = 42°
----------------------------------------------------------
tan48° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{18}{a}[/tex]
Multiply both sides by a
a × tan48° = 18 ( divide both sides by tan48° )
a = [tex]\frac{18}{tan48}[/tex] ≈ 16.2 ( to the nearest tenth )
-----------------------------------------------------------
sin48° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{18}{c}[/tex]
Multiply both sides by c
c × sin48° = 18 ( divide both sides by sin48° )
c = [tex]\frac{18}{sin48}[/tex] ≈ 24.2 ( to the nearest tenth )
What’s the value of m?
Answer: The answer is....I don't remember how to do this sort of problem...... sorry.....
Step-by-step explanation: So the three angles of a triangle equal to 180°.
First you have to find the angle that's missing besides "m"
Second add together the two angles you have.
Then You subtract the sum from 180.
Finally you have your answer.
LOOKING FOR BRAINLIEST !!Ashton surveyed some of the employees at his company about their cell phone habits. From the data, he concluded that most employees at his company use cell phones primarily for business. For which sample could this generalization be valid?
A.
all managers in the company
B.
some managers and some sales executives selected at random
C.
every fifth employee on the employee list
D.
every other sales executive on the employee list
PLZ Help Picture included. Thanks+brainlyest is correct.
Answer: [tex]\angle GFH[/tex]
Step-by-step explanation:
A Transversal is defined as a line that intersect two or more lines.
For this exercise it is important to know that when a Transversal cut two parallel lines, several angles are formed. These are grouped in pairs.
One of those pairs are called "Alternate exterior angles".
Alternate exterior angles are those non-adjacent angles that are located outside the parallel lines and on opposite sides of the Transversal.
Alternate exterior angles are congruent, which means that they have equal measure.
In this case you know that the Transversal [tex]CH[/tex] cuts the parallel lines [tex]AD[/tex] and [tex]EG[/tex].
Therefore, based on the explanation given before, you can identify in the picture given in the exercise that the angles [tex]\angle ABC[/tex] and [tex]\angle GFH[/tex] are Alternate exterior angles.
Which of these equivalent
ratios is the unit rate?
90 miles
3 hours
60 miles
2 hours
30 miles
1 hour
Answer:
30 miles/1 hour is the unit rate.
Step-by-step explanation:
This is the unit rate because unit rates are a number over 1 unit. 30 miles/1 hour fulfills that, and the others are 2 and 3 hours.
Write each decimal as a fraction in simplest form
0.8
Answer:
4/5
Step-by-step explanation:
.8 is the same as 8/10
8/10 simplifies to 4/5 as both the numerator and denominator can be divided by 2
Answer:
Step-by-step explanation:
0.8 = 8/10 = 4/5
Carmen often orders party trays from her favorite Mexican food restaurant For company events. For a recent company party, she spent $58 on one burrito platter and one taco platter. For a company meeting, she spent $90 on to burrito platters and one taco platter. How much does each type of platter cost?
By setting up a system of equations from the given scenarios, we find that the cost of a burrito platter is $32 and the cost of a taco platter is $26.
Explanation:To solve Carmen's problem about the cost of burrito and taco platters, we need to set up a system of equations based on the information given.
We know she spent $58 on one burrito platter and one taco platter and $90 on two burrito platters and one taco platter.
Let's denote the cost of a burrito platter as B and the cost of a taco platter as T.
Step 1: Establish the Equations
The first scenario gives us the equation: B + T = 58.
The second scenario gives us the equation: 2B + T = 90.
Step 2: Solve the Equations
From the first equation, we can express T in terms of B: T = 58 - B.
Substitute the expression for T in the second equation: 2B + (58 - B) = 90.Simplify and solve for B: B = 32.Substitute the value of B back into any of the original equations to find T: T = 26.Therefore, the cost of a burrito platter is $32 and the cost of a taco platter is $26.
Use substitution to solve the system of linear equations. In your final answer, include all of your work.
y = -3x + 4
y + 1/3y = 4/3
The solution is [tex](1,1)[/tex]
Step-by-step explanation:
The system of linear equation is
[tex]y=-3x+4[/tex] and [tex]y+\frac{1}{3} y=\frac{4}{3}[/tex]
Using substitution method, let us substitute [tex]y=-3x+4[/tex] in the equation
[tex]y+\frac{1}{3} y=\frac{4}{3}[/tex]
[tex]-3 x+4+\frac{1}{3}(-3 x+4)=\frac{4}{3}[/tex]
Multiplying the term [tex]-3x+4[/tex] by [tex]\frac{1}{3}[/tex], we get,
[tex]-3 x+4-x+\frac{4}{3}=\frac{4}{3}[/tex]
Subtracting both sides by [tex]\frac{4}{3}[/tex],
[tex]-3x+4-x=0[/tex]
Simplifying, we get,
[tex]\begin{aligned}-4 x+4 &=0 \\-4 x &=-4 \\x &=1\end{aligned}[/tex]
Now, substitute [tex]x=1[/tex] in [tex]y=-3x+4[/tex]
[tex]y=-3(1)+4\\y=-3+4\\y=1[/tex]
Thus, the solution is [tex](1,1)[/tex]
Answer:
y = -3x + 4
x + 1/3y = 4/3
Substitute the first expression into the second equation for y:
x + 1/3(-3x + 4) = 4/3
x - x + 4/3 = 4/3
4/3 = 4/3
Thus, all real numbers are solutions.
Step-by-step explanation:
HOPE THIS HELPS, GOOD-LCK, and Brainliest, also let me know if i am wrong.
Writing and graphing linear equations
Answer:
whats the question?
Step-by-step explanation:
Given Angle 1 = Angle 2,
find x.
Answer:
x = 6
Step-by-step explanation:
Given ∠ 1 = ∠ 2 then the segment is an angle bisector and the ratios of sides to base are equal, that is
[tex]\frac{3}{x-4}[/tex] = [tex]\frac{x}{4}[/tex] ( cross- multiply )
x(x - 4) = 12 ← distribute left side
x² - 4x = 12 ( subtract 12 from both sides )
x² - 4x - 12 = 0 ← in standard form
(x - 6)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 2 = 0 ⇒ x = - 2
However, x > 0 , thus x = 6
Choose Yes or No to tell if the fraction
3
5
will make each equation true.
7
20
+
□
=
19
20
□
+
3
10
=
3
15
1
2
+
2
3
=
□
1
10
+
1
2
=
□
can someone please answer this for me thank you
The fraction 3/5 makes only the fourth equation true when added with the existing fractions. The first three equations do not yield true results when 3/5 is added.
Explanation:In Mathematics, when dealing with fractions, we need to maintain the rules of basic arithmetic, meaning that equal sums must be identical on both sides of the equation. Let's check each of these equations with the fraction 3/5:
Equation 1: 7/20 + 3/5 = 14/20 + 12/20 = 26/20 ≠ 19/20. So, the answer is 'No'.
Equation 2: 3/5 + 3/10 = 12/20 + 6/20 = 18/20 ≠ 3/15. So the answer is 'No'.
Equation 3: 1/2 + 2/3 ≠ 3/5. So the answer is 'No'.
Equation 4: 1/10 + 1/2 = 2/20 + 10/20 = 12/20 = 3/5. So the answer is 'Yes'.
Learn more about fractions here:https://brainly.com/question/10354322
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A line passes through the point (4,-7) and has a slope of 3/2. Write an equation in point-slope form for this line.
Answer:
Step-by-step explanation:
y - y1 = m(x - x1)
slope m = 3/2, y1 = -7, x1 = 4
y + 7 = 3/2(x - 4)
y + 7 = 3x/2 - 6
y = 3x/2 - 6 - 7
y = 3x/2 - 13
What is the slope of the line shown below?
(5, 1)
(-3, -1).
Answer:
I believe it is 1/4
Sorry if I am wrong
the answer is 1/4
this is from apx :))
It took mr. Raleigh a total of 9 hours to drive to his grandpa’s house. He drove m miles before lunch 240 miles after lunch. If he drove at a constant speed, what expression can be used to find how many miles Mr.Raleigh drove each hour?
What is the total cost of 1.9 cubic meters of soil if it sells for $40
Answer:
Step-by-step explanation:
Total cost = 1.9* 40 = 76.0 = $76
When unit rate is given,multiply.
The total cost of 1.9 cubic meters of soil is $76. This is calculated by multiplying the amount of soil bought (1.9 cubic meters) by the cost of one cubic meter of soil ($40).
Explanation:To calculate the total cost, we have to multiply the amount of soil bought (in cubic meter) by the cost of one cubic meter of soil. Here, the student is buying 1.9 cubic meters of soil and the cost of one cubic meter of soil is $40.
So, Total cost = amount of soil * cost of one cubic meter of soil
= 1.9 * 40
= $76
Therefore, the total cost of 1.9 cubic meter of soil is "$76."
Learn more about Cost calculation here:https://brainly.com/question/34783456
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Use 10 for m. Then find the value of the expression 3.5m.
Answer:
30
Step-by-step explanation:
the required ans 30 or the valuse is 30
A college with a graduating class of 4000 students in the year 2008 predicts that its graduating class
will grow 5% per year. Write an exponential function to model the number of students y in the graduating class t years
after 2008.
Answer:
[tex]y=4000*(1.05)^t[/tex]
Step-by-step explanation:
The graduating class grows by 5% each year, this means after 1 year the number of students graduating will be 105% of 4000, or
[tex]4000*\frac{105}{100} =4000*1.05[/tex]
And after 2 years it will be
[tex](4000*1.05)*1.05[/tex]
and so on. Thus, after [tex]t[/tex] years the number of students [tex]y[/tex] will be
[tex]\boxed{ y=400*(1.05)^t}[/tex]
An exponential function to model the number of students y in the graduating class t years after 2008 is y = 4000(1.05)^t
Exponential functionsThe standard exponential function is expressed as:
y = ab^x
a is the initial populationb is the rate x is the timeIf a college with a graduating class of 4000 students in the year 2008 predicts that its graduating class will grow 5% per year, hence the required exponential equation will be:
y = 4000(1.05)^t
Learn more on exponential function here: https://brainly.com/question/12940982
In the piece-wise function graphed below, which is the correct equation for when − 2 ≤ x ≤ 2
y=-2x+2
y=-1/2x+2
y=-2x+4
y=-1/2x+4
Answer:
y=-1/2x+2
Step-by-step explanation:
y = mx + p
m=slope = -1/2
p= y-intercept = 2
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 2
Step-by-step explanation:
The segment for - 2 ≤ x ≤ 2 is a straight line
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (2, 1) ← the endpoints of the line
m = [tex]\frac{1-3}{2+2}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, 2) ⇒ c = 2
y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation for - 2 ≤ x ≤ 2
what is the answer for the question 20.x+90
Answer:
20.x + 90 = 110.x
SOLVE THE EQUATION
j-5=3.4
j=?
What is 2 3/4 • 6 2/3
Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
(8π -8√3) cm²
Step-by-step explanation:
The area of a circle with radius 4 cm is given by ...
A = πr² = π(4 cm)² = 16π cm².
The red shaded portion is part of a semicircle. That semicircle will have an area half that of the circle, so ...
A/2 = 8π cm²
__
The triangle OCB is an equilateral triangle, so the angle at B is 60°. The side AC is then √3 times side BC*, so is 4√3 cm. The area of triangle ABC is then ...
A = (1/2)AC·BC = (1/2)(4√3 cm)(4 cm) = 8√3 cm²
This area is subtracted from that of the semicircle to obtain the red shaded area:
red area = semicircle area - triangle area
red area = (8π -8√3) cm²
____
* AC can be found either from the Pythagorean theorem (√(8²-4²)), using trig functions (4tan(60°)), or using your knowledge of 30°-60°-90° triangles.
What is the x intercept and y intercept of this equation.
Answer:
x intercept is 15 and y intercept is -3.75
Step-by-step explanation:
The first thing is to form equation with the given tow point using the formula
y-y1/x - x1 = y2 - y1/ x2 - x1
y + 5/x + 5 = -2 + 5/7 + 5
y + 5/x + 5 = 3/ 12
3x + 15 = 12y + 60
12y - 3x = -45
On x intercept y = 0
x = 15
On y intercept x = 0
y = -3.75
Given: F(x) = 3x^2+1, G(x) = 2x - 3, H(X) = x
Find F(x) + G(x) =
[tex]F(x)+G(x)=3x^2+2x-2.[/tex]
Solution:
Given data: [tex]F(x)=3x^2+1[/tex] and [tex]G(x)=2x-3[/tex]
To find F(x) + G(x):
Adding two functions which gives another function.
Substitute F(x) and G(x), we get
[tex]F(x)+G(x)=(3x^2+1)+(2x-3)[/tex]
[tex]=3x^2+1+2x-3[/tex]
[tex]=3x^2+2x-3+1[/tex]
[tex]=3x^2+2x-2[/tex]
[tex]F(x)+G(x)=3x^2+2x-2[/tex]
Hence, [tex]F(x)+G(x)=3x^2+2x-2.[/tex]
How do I solve this?
Answer:
The equation of the required straight line is y = 4x + 1.
Step-by-step explanation:
The equation of all the straight lines that are parallel to the straight line y = 4x - 3 is given by
y = 4x + c .............. (1)
where, c is any real constant and c ≠ - 3.
{Since parallel straight lines have the same slope and different y-intercept }
Now, we have to find the value of c such that the parallel straight line passes through the point (-1,-3).
Now, putting x = - 1 and y = - 3 in equation (1) we get,
- 3 = 4(- 1) + c
⇒ c = 1
Therefore, the equation of the required straight line is y = 4x + 1. (Answer)
In the standard (x,y) coordinate plane, what is the slope of the line joining the points (5,4) and (2,-7)?
Answer:
slope = [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (2, - 7)
m = [tex]\frac{-7-4}{2-5}[/tex] = [tex]\frac{-11}{-3}[/tex] = [tex]\frac{11}{3}[/tex]