Solve the following system of equations graphically.
y=3x+4
y=-2x-5
Answers
Answer:
(x, y) = (-1.8, -1.4)
Step-by-step explanation:
Related Questions
Help me plz I would really appreciate it!
Answers
Hope you could get an idea from here.
Doubt clarification - use comment section.
What is the range of possible sizes for side x?
Answers
Answer:
x = 3.96
Step-by-step explanation:
apply the pitagoras theorem
x =
[tex] \sqrt{ {2.8}^{2} + {2.8 }^{2} } [/tex]
I just need the answer to the first question (16) plz thx
A)Evaluate g(0)
B)Find x if g(x)=0
C) domain and range
Answers
Answer:
a) g(0) = -4
b) x = -2 or +2 for g(x) = 0
c) domain: all real numbers; range: y ≥ -4
Step-by-step explanation:
a)g(0) is the value of the function when x=0. That is where the function crosses the y-axis. g(0) = -4.
__
b)g(x) = 0 where the graph crosses the x-axis. The x-values there are ...
x = -2 and x = 2
__
c)The domain is the horizontal extent of the graph. Here, we assume the graph extends to infinity both in the upward direction and to the left and right. Thus the horizontal extent (domain) is from -∞ to +∞, or "all real numbers."
The point where the graph crosses the y-axis is a minimum. There are no y-values below that point. So, the vertical extent (range) of the graph is from y=-4 to +∞.
y ≥ -4 . . . . range
A town has two shopping malls. A survey conducted on the shopping preferences of the town's residents showed that 62% of the residents visit Comet Mall, 73% of the residents visit Star Mall, and 48% of the residents visit both malls. The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is
Answers
Using Venn probabilities, it is found that:
The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is 0.87 = 87%.In this problem, the events are:
Event A: Visits Comet Mall.Evenet B: Visits Star Mall.In this problem:
62% of the residents visit Comet Mall, hence [tex]P(A) = 0.62[/tex].73% of the residents visit Star Mall, hence [tex]P(B) = 0.73[/tex].48% of the residents visit both malls, hence [tex]P(A \cap B) = 0.48[/tex]The probability of either is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Hence:
[tex]P(A \cup B) = 0.62 + 0.73 - 0.48 = 0.87[/tex]
The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is 0.87 = 87%.You can learn more about Venn probabilities at https://brainly.com/question/25698611
Answer:
87%.
Step-by-step explanation:
The probability that a resident chosen at random shops at either Comet Mall or at Star Mall is 87%.
Samir bought 6 equally priced pencils for $2.10.
How much will 10 of these pencils cost?
$1.26
$2.63
$2.86
$3.50
Answers
Price of 6pencils=2.10
Price of one pencil
[tex]\\ \sf\longmapsto 2.10/6=0.35[/tex]
Price of 10pencils
[tex]\\ \sf\longmapsto 0.35(10)=\$3.5[/tex]
The cost of ten pencils is $3.50.
Given
Samir bought 6 equally priced pencils for $2.10.
Unit rate;A rate is a ratio that is used for comparing two different kinds of quantities which have different units.
The cost of 1 pencil is;
[tex]\rm =\dfrac{2.10}{6}\\\\=0.35[/tex]
Therefore,
The cost of 10 pencils is;
[tex]= 10 \times 0.35\\\\=3.50[/tex]
Hence, the cost of ten pencils is $3.50.
To know more about unit rate click the link given below.
https://brainly.com/question/11258929
If the actual sale for the week is $525 and hector guessed $625, what i the percent error?
Answers
Answer:
19.0% (1dp)
Step-by-step explanation:
$625-$525=$100
$100/$525=4/21×100=19.0% (1dp)
A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of the container costs $5/m2 to construct whereas the top and sides cost $3/ m2 to construct. Use Lagrange multipliers to find the dimensions of the container of this size that has the minimum cost
Answers
The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
The given parameters are:
Volume = 480m^3Cost: $5 per square meter for the bottom, and $3 per square meter for the sides.Assume the dimensions of the container are: x, y and z.
The volume (V) would be:
[tex]V = xyz[/tex]
Substitute 480 for V
[tex]xyz =480[/tex]
And the objective cost function would be:
[tex]C =8xy + 6xz + 6yz[/tex]
Differentiate the cost function using Lagrange multipliers
[tex]8x + 6z = \lambda xz[/tex]
[tex]8y + 6z = \lambda yz[/tex]
[tex]6x + 6y = \lambda xy[/tex]
Divide equation (1) by (2)
[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]
[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]
Factor out 2
[tex]\frac{4x + 3z}{4y + 3z} = \frac{x}{y}[/tex]
Cross multiply
[tex]4xy + 3yz = 4xy + 3xz[/tex]
Evaluate the like terms
[tex]3yz = 3xz[/tex]
Divide both sides by 3z
[tex]y = x[/tex]
Divide the first equation by the third
[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]
[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]
Factor out 2
[tex]\frac{4y + 3z}{3x + 3y} = \frac{z}{x}[/tex]
Cross multiply
[tex]4xy+3xz = 3xz + 3yz[/tex]
Cancel out the common terms
[tex]4xy = 3yz[/tex]
Divide both sides by y
[tex]4x = 3z[/tex]
Make z the subject
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
Recall that:
[tex]xyz =480[/tex]
Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
[tex]x \times x \times \frac 43x = 480[/tex]
So, we have:
[tex]\frac 43x^3 = 480[/tex]
Multiply both sides by 3/4
[tex]x^3 = 360[/tex]
Take the cube roots of both sides
[tex]x = \sqrt[3]{360}[/tex]
Recall that:
[tex]y = x[/tex]
So, we have:
[tex]y = \sqrt[3]{360}[/tex]
Also, we have:
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Read more about Lagrange multipliers at:
https://brainly.com/question/4609414
Find sin 90° + cos 360° + tan 0°
Answers
Answer:
2
Step-by-step explanation:
sin 90 is 1;
cos 360 is cos 0, or 1; and
tan 0 is 0.
Thus, sin 90° + cos 360° + tan 0° = 1 + 1 + 0 = 2
A half circle is joined to an equilateral triangle with side lengths of 12 units.
What is the perimeter of the resulting shape? Type your answer in the box below.
Answers
Answer:
P = 12 pi units + 24 units.
Step-by-step explanation:
All sides of an equilateral triangle are of the same length. Here that length is 12 units. We take a circle of diameter 12 units and cut it in half through its center. Finally, we join the triangle (remembering that all of the side lengths are 12 units) to the half circle of diameter 12 units.
The half circle portion of the resulting shape has circumference 2(pi)(12 units) divided by 2, or 12 pi units. This is half the formula C = 2(pi)(r). The two non-attached sides of the triangle have a total length of 24 units.
Thus, the perimeter of the resulting figure is P = 12 pi units + 24 units.
Determine the unit rate. Use mental math when you can. 6 golf balls for $15
Answers
Answer:
1 golf ball : $2.50
Step-by-step explanation:
You can first divide 6 and 15 by 3, and get 2 and 5.Then, you divide 5 by 2, which is 2.5Therefore, the unit rate is 1 golf ball : $2.50HURRRRRYYYYYYYY. I HAVE 5 MINUTES
Answers
Answer:
x = - 9/10
workings
2/3 x = - 3/5
multiply by 3/2 on both sides
x = - 9/10
Answer:
2/3x=-3/5
x=-3/5*3/2
x=-8/10
Luis made an error when he used the distributive property to write an equivalent expression.
Which sentence describes the error?
35x−15====(5⋅7)−(5⋅3)5(7−3)5(4)20
Answers
Answer:
35x does not equal 5 times 7Step-by-step explanation:
The second step ''(5 × 7) - (5 × 3)'' has an error.
Given that;
Luis made an error when he used the distributive property to write an equivalent expression.
Here the expression is,
35x - 15
It can be written as;
(5 × 7)x - (5 × 3)
Take 5 as common,
5 (7x - 3)
Therefore, the second step ''(5 × 7) - (5 × 3)'' has an error.
To learn more about the equation visit:
brainly.com/question/28871326
#SPJ3
PLEASE NO LINKS AND NO NEGATIVITY
Answers
Answer:
$1.20 per chicken
Step-by-step explanation:
[tex]\frac{money} {chickens}[/tex]
[tex]\frac{18}{15}[/tex]
1.2
__________________________________________________________
Hope this helps!!
If I am wrong, please tell me, I enjoy learning from my mistakes:)
how do I dilate triangles using scale factors? step by step
Answers
Answer:
so first you
Step-by-step explanation:
find the center point of dilation and measure the distance from this center point to a point on the preimage and also the distance from the center point to a point on the image.
Can someone answer this no bots please I will give you brainliest… please
Answers
Answer: Alice
Step-by-step explanation: Alice won because she started furthest From the starting line.
Please help ASAP. Trigonometry
Write TWO different equations that you could use to solve for x. You don't need to solve.
Answers
Answer:
cos(52°) = 18/x
x = 18·sec(52°)
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Cos = Adjacent/Hypotenuse
In this geometry, that means ...
cos(52°) = 18/x
You can use the relation sec(x) = 1/cos(x) to rewrite this as ...
x = 18·sec(52°)
_____
You can also use the complementary angle and the complementary trig function.
sin(90° -52°) = 18/x
Which one cuz they are in different order.!!!
Answers
Answer:
wot
Step-by-step explanation:
The sum of two numbers is 25. One number is twice the seond number plus seven.
What are the two numbers?
Answers
because 6x2=12
12+7=19
19+6=25
Does anyone know how to answer this?
Answers
The length of the rectangle 4cm and the breadth is 3cm
Area of rectangle= length * breadth
Area= 4*3
= 12cm^2
Hope it helped
Step-by-step explanation:
We first calculate the lenght of the diameter, that is also the lenght of the hypotenuse of the right triangle shown in the figure:
d = [tex]\sqrt{3^2 + 4^2} = \sqrt{25} = 5[/tex] cm
The radius of the circle will be half of the diameter: r = d/2 = 2.5 cm
The area of the circle will be: Acircle = pi * r^2 = pi * 6.25 cm^2 = 19.6 cm^2 (circa).
Now from the area of the circle we subtract the area of the square:
Asquare = 4cm * 3cm = 12cm^2
A shaded = Acircle - Asquare = 19.6 cm^2 - 12cm^2 = 7.6 cm^2
Calculate the area of the triangular region determined by the points D(-4,3) E(-7,-8) F(-2, -3)
Answers
Answer:
The area is 27
Step-by-step explanation:
Area =1/2 [x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]
Area =1/2 [2(-6 - 8) + 3(8 - 4) + 7(4 + 6)]
=1/2 [2(-14) + 3(4) + 7(10)]
=1/2 (-28 + 12 + 70)
=1/2 (54)
Area = 27
4. It takes Zack 30 minutes to walk 7.5 blocks to the swimming pool. At this rate, how many blocks can he walk in
one minute?
A. 1 block
30
B. block
7.5
765-30.5775
C. 4 blocks
D.) 5 blocks
Answers
Answer:
He can walk 0.25 blocks in 1 minute
Step-by-step explanation:
If Zack can walk 7.5 blocks in 30 minutes and we are looking for how many blocks he can walk in 1 minute, we will divide 7.5 by 30 as that will be the number of blocks per minute.
7.5/30 = 0.25
According to building codes, a wheelchair ramp should have a slope of 1/10 or less.
a) Does the wheelchair ramp shown meet the requirements? (The ramp had a height of 75 cm and a length of 800 cm.)
Include calculations to justify your answer.
Answers
Using the slope formula, it is found that the slope is of 0.09375 < 0.1, hence, it meets the requirements.
The slope of a ramp is given by it's height divided by it's length, that is:
[tex]m = \frac{h}{l}[/tex]
In this problem:
The height is of 75 cm, hence [tex]h = 75[/tex].The length is of 800 cm, hence [tex]l = 800[/tex].Then, the slope is given by:
[tex]m = \frac{h}{l} = \frac{75}{800} = 0.09375[/tex]
The slope is of 0.09375 < 0.1, hence, it meets the requirements.
A similar problem about the use of slopes in ramps is given at https://brainly.com/question/18090623
The shortest route from London to Swansea is 180 miles. A lorry is expected to take 4.5 hours to travel this route. The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 4.5 hours. By how many more mph than the expected speed does the lorry travel?
Answers
Answer:
6mph
Step-by-step explanation:
180/4.5=40
180 × (1+15%)=207
207/4.5=46
46-40=6
what is the equation of the line with slope -7 which goes through the point (2,5)
Answers
Answer:
y=-7x+19
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-7(x-2)
y=-7x+14+5
y=-7x+19
The equation of the line with slope - 7 which goes through the point (2, 5) is
y = - 7x - 19.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, A line passes through points (2, 5) with a slope of - 7.
∴ 5 = -7(2) + b in slope-intercept form.
5 = - 14 + b.
b = - 19.
y = - 7x - 19.
learn more about lines and slopes here :
https://brainly.com/question/3605446
#SPJ5
The sum of three consecutive odd numbers is 99.
What is the smallest of the three numbers ?
Answers
31
hope this is helpful!
Simplify.
(–28xy) ÷ (–4)
−7xy
17ab
−17ab
7xy
Answers
If any doubt leave a comment
Solve for C: 20 (greater than or equal too sign) C-11
Answers
Answer:
C (is greater than it equal to) 31
Step-by-step explanation:
Isolate the c by adding 11 to both sides (cancels out the 11 and turns 20 into 31). Keep the sign the same!! Hope this helped! <33
Segment AB and CD intersect at point E, measure of angle ABC =6x+20 and measure of angle DEB=10x. What is the value of x?
Answers
Answer:
x = 5
Step-by-step explanation:
6x + 20 = 10x
I hope this helps!
3y=6
Find the slope of the line described by each equation
Answers
But I think the slope is 0
Please correct me if I’m wrong.
In right â†LMN, sin M = 0. 759. What is cos N? A. 0. 121 B. 0. 241 C. 0. 349 D. 0. 651 E. 0. 759.
Answers
The correct option is E. 0.579
Given, sin M = 0.759.
We have to find the value of cos N.
Since [tex]\Delta LMN[/tex] is right triangle.
We know that,
[tex]sin(90-\Theta)= Cos \Theta[/tex]
Assuming L is the right angle, So the other two angles are complementary.
Thus, [tex]cos(N) = sin(90-N) = sin(M)[/tex]
Hence,[tex]Cos(N)=Sin(M)[/tex]
Therefore the value of Cos N will be 0.759.
For more details on trigonometric ratio follow the link:
https://brainly.com/question/1201366