Answer:
[tex]\large\boxed{y=\dfrac{15}{14}x+1.5}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
------------------------------------------------------------------------
You must solve the system of equations:
[tex]\left\{\begin{array}{ccc}4x-3y+4=0&(1)\\x+2y=5&(2)\\y=mx+1.5&(3)\end{array}\right\qquad\text{substitute (3) to (1) and (2)}\\\\\left\{\begin{array}{ccc}4x-3(mx+1.5)+4=0\\x+2(mx+1.5)=5\end{array}\right\qquad\text{use the distributive property}\\\left\{\begin{array}{ccc}4x-3mx-4.5+4=0\\x+2mx+3=5&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx-0.5=0&\text{add 0.5 to both sides}\\x+2mx=2\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx=0.5&\text{multiply both sides by 2}\\x+2mx=2&\text{multiply both sides by 3}\end{array}\righ[/tex]
[tex]\underline{+\left\{\begin{array}{ccc}8x-6mx=1\\3x+6mx=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad11x=7\qquad\text{divide both sides by 11}\\.\qquad x=\dfrac{7}{11}\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\\dfrac{7}{11}+2m\left(\dfrac{7}{11}\right)=2\qquad\text{multiply both sides by 11}\\\\7+2m(7)=22\qquad\text{subtract 7 from both sides}\\\\14m=15\qquad\text{divide both sides by 14}\\\\m=\dfrac{15}{14}[/tex]
for questions 5-6 the functions are
f(x)=5x^2+3
g(x)=x^2-7
Answer:
see explanation
Step-by-step explanation:
Note that
(f + g)(x) = f(x) + g(x) and
(f - g)(x) = f(x) - g(x)
5
f(x) + g(x)
= 5x² + 3 + x² - 7 = 6x² - 4
6
f(x) - g(x) = 5x² + 3 - (x² - 7) ← distribute parenthesis
= 5x² + 3 - x² +7 ← collect like terms
= 4x² + 10
7
f(x) + g(x) = [tex]4^{x}[/tex] + 3x + 2x - 5 = [tex]4^{x}[/tex] + 5x - 5
Which statement best describes triangles UWW and
XYZ?
Answer:
Similar but not congruent
Step-by-step explanation:
For them to be congruent, they have to have same everything but not necessarily the same orientation. They are not congruent because their corresponding sides aren't the same measurement.
You can tell if two triangles are similar if each pair of corresponding are congruent.
They will also have corresponding sides are proportional.
That is 50/40=60/48=40/32 in this case? Well does it? It does, because each one of them is equal to 1.25.
Answer:
The correct answer is second option
They are similar, but not congruent
Step-by-step explanation:
From the given diagram we can see two triangles.
ΔUVW and ΔXYZ
m<X = m<U,
m<Y = m<V and
m<Z = m<W
Therefore two triangles are similar
The sides of these two triangles are not congruent, therefore these two triangles are not congruent.
The correct answer is second option
They are similar, but not congruent
mike is 7.5 miles ahead of julia running at 5.5 miles per hour and julia is running at the speed of 6 miles per hour.How long does it take julia to catch mike.
The answer is 15 hours but I am unsure as to why,can someone explain?
Answer:
15 hours.
Step-by-step explanation:
Suppose the time taken to catch Mike is t hours and the distance ran by Mike is x miles then
5.5 = x/ t (Mike) --- ...(1)
6 = (x +7.5 )/ t (Julia ).......(2)
From equation (1):
x = 5.5t ..............(3).
From equation (2):
x + 7.5 = 6t
x = 6t - 7.5............(4).
Eliminating x from equations 3 and 4:
6t - 7.5 = 5.5t
0.5t = 7.5
t = 15 hours.
What is the length of cord AB
Answer:
CE = 16
Step-by-step explanation:
From my understanding, the length of cord AB is given. According to the question in the picture attached, you need to find CE.
Triangle ABD and triangle ACE are similar.
Therefore, AB/AC = BD/CE
AB = 6, AC = 8, BD = 12, CE = ?
6/8 = 12/CE
CE = 12x8/6
CE = 16
Therefore, CE is equal to 16.
!!
Rachel is going to calculate the following expression: 3.32/1.66+18.4. She calculates the expression as it is written and then writes down the answer rounded to the nearest whole number. She then calculates it again, but rounds each of the 3 numbers in the expression to the nearest integer, and then performs the division and addition. She writes this answer down next to the answer she got before. What is the positive difference between the 2 answers she got?
Answer:
the answer is 0.5 lol
3. Write an equation in point-slope form for the line through the given point with the given slope.
(4, -6); m = 3/5
A. Y-4=3/5x (x+6)
B. Y+6=3/5(x-4)
C. Y+6=3/5x-4
D. Y-6=3/5(x+4)
Answer:
B
Step-by-step explanation:
recall that point-slope form of a linear equation is expressed as follows
y - y1 = m (x - x1)
where m = slope and (x1, y1) is the coordinate of any point on the line
so, here we have m = (3/5), x1 = 4 and y1 = -6
substitute these into the formula
y - (-6) = (3/5) (x - 4)
y + 6 = (3/5) (x - 4)----> answer
Answer:
[tex]\boxed{\text{B. }y + 6 =\dfrac{3}{5}(x - 4)}[/tex]
Step-by-step explanation:
The point-slope formula for a straight line is
[tex]y - y_{1} = m(x - x_{1})[/tex]
x₁ = 4; y₁ = -6; m = ⅗
Substitute the values
[tex]\begin{array}{rcl}y - (-6) & = & \dfrac{3}{5}(x - 4)\\\\y + 6 & = & \dfrac{3}{5}(x - 4)\\\\\end{array}\\\text{The equation for the line is $\boxed{\mathbf{y + 6 =\dfrac{3}{5}(x - 4)}}$}[/tex]
The figure shows the graph of the equation with slope ⅗ passing through (4,-6).
How many solutions does the nonlinear system of equations graphed below
have?
A. One
B. Two
C. Four
D. Zero
Putting two or more equations in a system means to find the set of variables that satisfies all the equations at the same time.
Moreover, the points that satisfy an equation are the points that lay on the graph described by the equation.
So, putting everything together, solving a system means to lay on all the graphs at the same time. In other words, the solutions of a system are the points of intersection between the graphs that represent the functions involved in the system.
In this case, the line and the circumference have two points of intersection, and they are the two solutions of the system.
In the absence of the graph, one can still note that the number of solutions a nonlinear system of equations has depends on the points of intersection of the curves represented by the equations. Each point of intersection represents a solution.
Explanation:Unfortunately, without the graph, it is rather difficult to directly answer how many solutions the nonlinear system of equations has. In general, the number of solutions for a nonlinear system of equations can be determined by where the curves represented by the equations intersect. The point of intersection is considered a solution. This is because at this point both equations hold true. If the curves intersect once, then there is one solution. If they intersect twice, then there are two solutions. If they never intersect, there are zero solutions.
Learn more about nonlinear system of equations here:https://brainly.com/question/13594448
#SPJ5
Whitch expression is equivlent to the expression
7(3x-2) + 4(x+5)
Answer:
[tex]\large\boxed{7(3x-2)+4(x+5)=25x+6}[/tex]
Step-by-step explanation:
[tex]7(3x-2)+4(x+5)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(7)(3x)+(7)(-2)+(4)(x)+(4)(5)\\\\=21x-14+4x+20\qquad\text{combine like terms}\\\\=(21x+4x)+(-14+20)\\\\=25x+6[/tex]
Answer:
[tex]\Huge \boxed{25x+6}[/tex]
Step-by-step explanation:
[tex]\large \textnormal{Distributive property}[/tex], [tex]\large \textnormal{A(B+C)=AB+AC}[/tex].
[tex]\displaystyle 7(3x-2)=21x-14[/tex]
[tex]\displaystyle 21x-14+4(x+5)[/tex]
[tex]\displaystyle 4(x+5)=4x,5\times 4=20, 4x+20[/tex]
[tex]\Large\textnormal{Solve to find the answer.}[/tex]
[tex]\displaystyle 21x-14+4x+20=25x+6[/tex]
[tex]\Large \textnormal{Correct answer is \boxed{25x+6}.}[/tex]
find the equivalent expression using the same bases (46 x 59)^6
Answer:
46^6 x 59^6
Step-by-step explanation:
For properties (axb)^y has the equivalent expression of a^y x b^y
Then, (46x59)^6 can be written as 46^6 x 59^6
Answer: [tex]46^6* 59^6[/tex]
Step-by-step explanation:
Given the expression [tex](46* 59)^6[/tex], in order to find an equivalent expression using the same bases, you need to remember the following:
[tex](a*b)^n=a^n*b^n[/tex]
So, you can observe that, in this case:
[tex]a=46\\b=59\\n=6[/tex]
Therefore, substituting values, you get the following equivalent expression:
[tex](46* 59)^6=46^6* 59^6[/tex]
Which is the standard form of the equation of the parabola that has a vertex of (3,1) and a directrix of x= -2?
Answer:
(y-1)^2=20(x-3)
Step-by-step explanation:
The parabola is sideways so the squared part will be on the y.
The equation will be using is (y-k)^2=4p(x-h)
where (h,k) is the vertex.
p tells us which way the parabola opens by the sign.
p also tells us how far the directrix is from the vertex or the vertex from the focus.
Anyways if you graph the vertex and the directrix you will see the parabola opens to the right so p is going to be positive.
Now since the directrix is at x=-2 and the vertex is at (3,1) then p=3-(-2)=5. 5 means that the directrix and vertex are 5 units apart.
The vertex was given as (3,1) so h=3 and k=1.
Let's plug this information in:
(y-1)^2=4*5(x-3)
Let's simplify just a little.
(y-1)^2=20(x-3)
Answer:
C
Step-by-step explanation:
on edge
Hey scale rounds the weight of object to the nearest 10th of a pound what amount would it around the following wait to
Round to the nearest 10th :
A) 53.864 pound ————
B) 14.62 pounds ————-
C) 608.97 pounds ———-
Please answer fast
{(1,2), (-2,3), (1,3), (-2,2)} is what type of relation?
A. one-to-many
B. many-to-many
C. one-to-one
D. many-to-one
Answer:
B. Many-to-many
Step-by-step explanation:
We have the following ordered pairs:
(1,2)(-2,3)(1,3)(-2,2)First let's define the following concepts:
One-to-one: A function is said to be one-to-one if every y value has exactly one x value mapped onto it.Many-to-one: If there are y values that have more than one x value mapped onto them.One-to-many: If there are x values that have more than one y value mapped onto them. (NOT A FUNCTION)Many-to-many: If there are x values that have more than one y value mapped onto them and at the same time, there are y values that have more than one x value mapped onto them (NOT A FUNCTION)From all the ordered pairs, we find that the points (1,2) and (1,3) have the same x-value for diferent y-values. Also we find that the points (1,2) and (-2, 2) have different x-values for the same y-value.
Therefore, the ordered pairs DO NOT belong to a function and can be considered MANY-TO MANY.
The given relation is a many-to-one relationship.
The given relation {(1,2), (-2,3), (1,3), (-2,2)} is an example of a many-to-one relationship. In a many-to-one relation, multiple elements in the domain map to a single element in the range. Each x-value has a unique y-value.
what is the slope of the line passing through the points (-5,9) and (2,-12)
Answer:
-3
Step-by-step explanation:
To find the slope of a line given two points, we use:
[tex]\frac{y_2-y_1}{x_2-x_1} \text{ when the points } (x_1,y_1) \text{ and } (x_2,y_2) \text{ are on the line }[/tex].
Or you could line up the points vertically and subtract the points vertically, then put 2nd difference over 1st difference.
That looks like this:
( 2 , -12)
-( -5 , 9 )
----------------
7 -21
So the slope is -21/7 which gives you -3.
Solve for k k/2 + 1/2 = 3
k/2+1/2=3
Move +1/2 to the other side. Sign changes from +1/2 to -1/2
k/2+1/2-1/2=3-1/2
k/2=3-1/2
Find the common denominator for 3 and -1/2.
Common denominator is 2
k/2=3(2)-1/2
k/2= 6/2-1/2
k/2=5/2
Multiply k/2 with 2. Multiply 2 with 5/2
k/2 (2/1)=2(5/2)
Cross out 2 and 2. Divide by 2. Cross out 2 and 2 for 5/2(2). Divide by 2
k=5
Simplify remove all the perfect squares from inside the square root 45
Answer:
3[tex]\sqrt5}[/tex]
The square root of 45 can be simplified by removing perfect square factors. In this case, the number 9 is a perfect square factor of 45, resulting in the simplification √45 to 3√5.
Explanation:To simplify the square root of 45 by removing perfect squares, we first need to identify the factors of 45 that are perfect squares. In this case, the number 9 is a factor of 45 and is a perfect square. Therefore, we can simplify √45 to √9*5 or 3√5. Simplifying square roots is a basic principle of Mathematics one should know as it is often applied in various middle school, high school, and even college math problems.
Learn more about Simplifying Square Roots here:https://brainly.com/question/1441039
#SPJ2
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
Dakota believes there is a correlation between the number of texts sent in class and GPA. She collected data and found that the line of best fit for the data can be modeled by the equation y = 3.9 − 0.3x.
Identify and interpret the slope in this scenario.
a. The slope is −3.9. Starting at 0.3, the GPA will decrease by 3.9 for every text sent in class.
b. The slope is 3.9. Starting at 0.3, the GPA will increase by 3.9 for every text sent in class.
c. The slope is 0.3. Starting at 3.9, the GPA will increase by 0.3 for every text sent in class.
d. The slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.
Answer:
d. The slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.
Step-by-step explanation:
You can write the equation is the slope intercept form of y=mx+c
where m is the slope and c in the y-axis intercept
write the equation as;
y=mx+c
y= -0.3x+3.9
Here , you have a negative slope which means the GPA will reduce by 0.3 for every text sent in class.
See attached graph to visualize the y-intercept point
Answer:
The correct option is d.
Step-by-step explanation:
The given equation of best fit line is
[tex]y=3.9-0.3x[/tex] .... (1)
The slope intercept form of a line is
[tex]y=mx+b[/tex] .... (2)
where, m is slope and b is y-intercept or initial value.
From (1) and (2), we get
[tex]m=-0.3[/tex]
[tex]b=3.9[/tex]
It means the slope is −0.3. Starting at 3.9, the GPA will decrease by 0.3 for every text sent in class.
Therefore the correct option is d.
Which of the following is the correct notation for the complex number
Answer:
1-4i
Step-by-step explanation:
[tex]i=\sqrt{-1}[/tex]
We have [tex]1-\sqrt{-16}[/tex].
Let's look at the [tex]\sqrt{-16}[/tex] part.
Since it has a negative inside the square root, it is imaginary. This is our imaginary unit [tex]i=\sqrt{-1}[/tex].
So [tex]\sqrt{-16}[/tex]
[tex]=\sqrt{16} i [/tex]
[tex]=4i[/tex]
So [tex]1-\sqrt{-16}=1-4i[/tex]
Square root of 4/(7-3i)+(2+5i)
you can do it ans is above
What is the approximate radius of a sphere whose volume is 1349 cm?
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=1349 \end{cases}\implies 1349=\cfrac{4\pi r^3}{3}\implies 4047=4\pi r^3 \\\\\\ \cfrac{4047}{4\pi }=r^3\implies \sqrt[3]{\cfrac{4047}{4\pi }}=r\implies 6.85\approx r[/tex]
Turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. Ben has sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. Let x represent the number of turkey sandwiches and y represent the number of veggie wraps. The inequality represents the food sales in the first hour. If Ben has sold 4 veggie wraps, what is the maximum value of turkey sandwiches Ben could have sold? 5 6 7 10
Answer:
The maximum number of turkey sandwiches Ben could have sold is 6.
Step-by-step explanation:
We are given that turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand.
Given the information, we are to find the maximum value of turkey sandwiches Ben could have sold.
[tex] 2 . 5 0 x + 3 . 5 0 y \leq 3 0 [/tex]
Number of veggie wraps sold (y) = 4
2.50x + 3.50(4) < 30
2.50x + 14 < 30
- 14 -14
2.50x < 16
[tex]x<\frac{16}{2.50}[/tex]
[tex]x <6.4[/tex]
The maximum number of turkey sandwiches Ben could have sold is 6.
The maximum value of turkey sandwiches Ben could have sold is;
Option B; 6
Let number of turkey sandwiches be x
Let number of veggie wraps be y.
We are told that Turkey sandwiches cost $2.50 and veggie wraps cost $3.50.
Thus, for x number of Turkey sandwiches, the cost will be; 2.5x
For y number of veggie wraps, the cost will be 3.5y.
We are told he sold no more than $30 worth of turkey sandwiches and veggie wraps in the first hour of business. Thus, inequality to represent this scenario is;
2.5x + 3.5y ≤ 30
Now, he has sold 4 veggie wraps. Thus;
2.5x + 3.5(4) ≤ 30
2.5x + 14 ≤ 30
2.5x ≤ 30 - 14
2.5x ≤ 16
x ≤ 16/2.5
x ≤ 6.4
Since the number can't be decimal, we approximate to a whole number to get; x = 6
Read more at; https://brainly.com/question/20308451
A savings account was opened with an initial deposit and never touched again. An account that does not meet the minimum
balance requirement is charged a service fee.
Assuming the account was open with an initial deposit below the minimum amount, the current account balance, B, is equal to the
product of the initial deposit, I, and the quantity of the difference of 1 and the monthly service fee, f, raised to the power of n, the
number of months since the account was open.
If an initial deposit of $2,586,00 is made to the account with a monthly service fee of 2% what will be the value of B after
19 months? Round to the nearest cent.
A.
$1,797.62
B. $1,603.32
C. $1,761.67
D. $3,767.31
What is the mean of the following numbers: 5, 7, 4, 4, 5, 4, 6?
35
5
4
6
Answer: 5
Step-by-step explanation: First, add all of the given numbers.
5+7+4+4+5+4+6=35
Next, divide 35 by the number of given numbers, which is 7.
35/7 = 5
The mean is 5.
how many 1/4s fit in 1/2
Answer:
2
Step-by-step explanation:
1/4+1/4=1/2
The variable z is directly proportional to x, and inversely proportional to y. When x is 16 and y is 5, z has the value 16. What is the value of z when x= 21, and y= 14 Round to at least the thousandths place if needed.
Answer:
z = 7.5
Step-by-step explanation:
Given that z is directly proportional to x and inversely proportional to y then the equation relating them is
z = [tex]\frac{kx}{y}[/tex] ← k is the constant of proportionality
To find k use the condition when x = 16, y = 5, z = 16, then
k = [tex]\frac{zy}{x}[/tex] = [tex]\frac{16(5)}{16}[/tex] = 5
z = [tex]\frac{5x}{y}[/tex] ← equation of proportionality
When x = 21, y = 14, then
z = [tex]\frac{5(21)}{14}[/tex] = 7.5
Which of the following is the equation of
the line passing through the points (1, 1)
and (-3,5)?
(A) y=x
(B) y= -x
(C) y= -1x – 2
(D) y= -1x + 2
Which of the following is the equation of a
line with a slope of 0 passing through (2,5)?
(A) x = 2
(B) x= -2
(C) y=5
(D) y= -5
Answer:
a) Option A is correct.
b) Option C is correct.
Step-by-step explanation:
a) Which of the following is the equation of the line passing through the points (1, 1) and (-3,5)?
We will use the equation
(y-y₁)=m(x-x₁)
m= (y₂-y₁)/(x₂-x₁)
m= (5-1)/(-3-1)
m= 4/-4
m= -1
Consider point (1,1) and Putting value of m
(y-y₁)=m(x-x₁)
(y-1)=1(x-1)
y-1=x-1
y=x-1+1
y=x
So, Option A is correct.
b) Which of the following is the equation of a line with a slope of 0 passing through (2,5)?
The formula used is:
y= mx+b
Finding b:
5=0(2)+b
=> b = 5
So, equation is:
y = mx+b
y=0x+5
y=5
So, Option C is correct.
Which of the following inequalities matches the graph?
[tex]x \leqslant 0[/tex]
[tex]x \geqslant 0[/tex]
[tex]y \leqslant 0[/tex]
[tex]y \geqslant 0[/tex]
which one is it 1,2,3,or the 4 one
Answer:
[tex]\large\boxed{x\leq0}[/tex]
Step-by-step explanation:
x ≤ 0 - the region below the line x = 0 (x axis)
x ≥ 0 - the region above the line x = 0 (x axis)
y ≤ 0 - the region on the left of the line y = 0 (y axis)
y ≥ 0 - the region on the right side of the line y = 0 (y axis)
all region with lines (axes)
We have the region below the x axis (x = 0).
What is the surface area of the figure?
314 in.2
792 in.2
628 in.2
546 in.2
Answer:
628 n.2 is the correct answer
Which term describes how the two sides of this figure are related?
O
A. Induction
O
B. Deduction
O
C. Symmetry
O
D. Scientific method
Answer:
The answer is A - symmetry.
None of the other options really have bearing in relation to the question.
Hope this helps.
Step-by-step explanation:
The given image shows the symmetry of a shape. Both the divided sides are equal halves of the shape. Therefore, option C, symmetry is correct option.
What is symmetry of a figure ?Symmetry is a property of a figure that describes how it looks the same after being transformed in a certain way. In other words, a figure is said to have symmetry if it can be divided into parts that are mirror images or identical to each other.
There are different types of symmetry, such as :reflection symmetry, rotational symmetry, translational symmetry etc.
Symmetry is an important concept in many areas of mathematics and science, such as geometry, crystallography, physics, and chemistry. It is also a fundamental aspect of beauty and aesthetics in art, architecture, and design.
The given figure can be divided into two equal halves. Hence, the two sides are in symmetry. Thus, option C is correct.
Find more on symmetry :
https://brainly.com/question/29044130
#SPJ7
Your complete question is attached below:
The temperature of a liquid increases the same amount over time. At the end of the first day, its temperature was 47 f and at the end of the third day, it was 51f The following line represents this situation. But the graph has some missing parts.
Answer:
It increases by 2 degrees every day
Step-by-step explanation:
51-47=4 4/2 equal 2