Question 1
The given system of equations is:
[tex]y = {x}^{2} + 5x + 6 \\ y = 3x + 6[/tex]
Equate the two equations:
[tex] {x}^{2} + 5x + 6 = 3x + 6[/tex]
Rewrite in standard form:
[tex] {x}^{2} + 5x - 3x + 6 - 6 = 0[/tex]
[tex] {x}^{2} + 2x = 0[/tex]
[tex]x(x + 2) = 0[/tex]
[tex]x = 0 \: or \: x = - 2[/tex]
When we put x=0, in y=3x +6, we get:
[tex]y = 3(0) + 6 = 6[/tex]
One solution is (0,6)
When we put x=-2, into y=3x+6, we get:
[tex]y = 3( - 2) + 6 = 0[/tex]
Another solution is (-2,0)
The solutions are; (0,6) and (-2,0)
Question 2:
The function is
[tex]f(x) = {x}^{6} - {x}^{4} [/tex]
Let us put x=-x,
[tex]f( - x) = {( - x)}^{6} - {( - x)}^{4} [/tex]
This gives:
[tex]f( - x) = {x}^{6} - {x}^{4} [/tex]
We can observe that:
[tex]f(x) = f( - x)[/tex]
This is the property of an even function.
Question 3:
The given function is
[tex]f(x) = {x}^{2} + 3x - 2[/tex]
The average rate of change of f(x) from x=a to x=b is given as:
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
This is the slope of the secant line connecting the two points on f(x)
From x=2 to x=6, the average rate of change
[tex] = \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11[/tex]
The average rate of change is 11
Solve (x+4)2 – 3(x + 4) – 3 = 0 using substitution.
u=
Answer:
Step-by-step explanation:
(x+4)2-3(x+4)-3=0
2x+8-3x-12-3=0
-1x-4-3=0
-1x-7=0
-1x=7
x=7/-1
x=-7
Answer:
u= x + 4
Step-by-step explanation:
I just did the as. and quiz
A container has a volume of 860 cm?.
Find its capacity.
Answer:
0.86liters
Step-by-step explanation:
860cm³=0.86dm³=0.86liters
The capacity of the container is 860 cm³.
To find the capacity of the container, we need to understand that the volume and the capacity are essentially the same thing when referring to containers.
The volume of a container is the amount of space it occupies, and the capacity is the amount of fluid or substance it can hold. Since the volume is already given in cubic centimetres (cm³), which is a unit of volume, it directly translates to the capacity of the container.
Therefore, without the need for any conversion or further calculation, we can state that the capacity of the container is 860 cm³. If one were to express this capacity in litres, knowing that 1 liter is equivalent to 1000 cm³, we could perform a conversion:
[tex]\[ \text{Capacity in liters} = \frac{\text{Capacity in cm}^3}{1000} \][/tex]
[tex]\[ \text{Capacity in liters} = \frac{860}{1000} \][/tex]
[tex]\[ \text{Capacity in liters} = 0.86 \][/tex]
So, the capacity of the container is 0.86 litres, which is equivalent to 860 cm³.
1. If you plot each of the points listed below on a Cartesian plane, the points will form a "picture"
of a geometric shape. What's the shape, and in which quadrant will it appear?
(-5
-6)
COCO
-6, -3)
(-9,-6)
Step-by-step explanation:
Based on the given points, we can plot them on a Cartesian plane and determine the resulting shape.The points are:
A: (-5, -6)
B: (0, 0)
C: (-6, -3)
D: (-9, -6)If we connect these points in the order ABCDA, we form a parallelogram.The parallelogram appears in the third quadrant (Quadrant III) of the Cartesian plane, as all the given points have negative x and y coordinates.
Expand and simplify 4(2x+4)+5(4x+3)
Answer:
see below
Step-by-step explanation:
4(2x+4)+5(4x+3)
Distribute
4*2x+4*4 +5*4x+ 5*3
8x+16 +20x +15
Combine like terms
28x +31
The diagram below shows scalene triangle JKL.
Which is true about the diagram? Select two options.
Measure of angle J K H + measure of angle J K L = 180 degrees
Measure of angle J K L + measure of angle J L K + measure of angle K J L = 180 degrees
Measure of angle J K H = measure of angle J L K
Measure of angle J K L + measure of angle J L K = 90 degrees
Measure of angle K J L = measure of angle K L J
The correct statement about the diagram is,
⇒ Measure of angle JKH + measure of angle JKL = 180 degrees
⇒ Measure of angle JKL + measure of angle JLK + measure of angle KJL = 180 degrees
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
The diagram is shown.
Now, By definition of linear pair of angles, we get;
⇒ m ∠JKH + m ∠JKL = 180°
And, The sum of angles in triangle is 180°
Hence, We get;
⇒ m ∠ JKL + m ∠ JLK + m ∠ KJL = 180 degrees
Thus, The correct statement about the diagram is,
⇒ Measure of angle JKH + measure of angle JKL = 180 degrees
⇒ Measure of angle JKL + measure of angle JLK + measure of angle KJL = 180 degrees
Learn more about the angle visit:;
https://brainly.com/question/25716982
#SPJ3
Are 4(x-3) and 6x-2(x-3) equivalent?
Answer:
No, 4x - 12 ≠ 4x + 6
Step-by-step explanation:
Step 1: Distribute both expressions
4(x - 3)
(4 * x) + (4 * -3)
(4x) + (-12)
4x - 12
6x - 2(x - 3)
6x - (2 * x) - (2 * -3)
6x - (2x) - (-6)
6x - 2x + 6
4x + 6
Answer: No, 4x - 12 ≠ 4x + 6
Answer:
No its not because when solved you get 4x-12The tables show the books read by two different students. Explain how to determine which student read faster.
The first student read faster than the second student.
Step-by-step explanation:
Step 1:
To determine how long each student takes to read a book, we divide the time taken to read by the number of books read in that period.
Time taken to read a book = [tex]\frac{time taken to read}{number of books read in that period}[/tex].
In the given table, the second column values are times taken to read and the first column represents the number of books read in that period.
Step 2:
For the first student, the time taken is calculated.
The first student's time taken to read a book = [tex]\frac{30}{3}[/tex] = [tex]\frac{50}{5}=\frac{70}{7}[/tex] = 10 minutes to read a book.
Step 3:
Similarly, the time taken to read a book is calculated for the second student.
The first student's time taken to read a book = [tex]\frac{24}{2}=\frac{48}{4}=\frac{72}{6}[/tex] = 12 minutes to read a book.
Step 4:
Now we compare the times taken. The first student read a book in 10 minutes while the second student took 12 minutes for a book. So the first student read faster.
16. CRITICAL THINKING
Two figures are congruent. Are the areas of the two figures
the same? the perimeters? Explain your reasoning.
Both area and perimeter are the same. They have the same shape and dimensions.
This is because congruency means that the two figures are identical, one is the clone of the other.
Two congruent figures have identical shape and size, meaning their perimeters and areas are both equal.
If two figures are congruent, this means that they are identical in shape and size. Congruent figures are essentially the same figure superimposed from one location to another. According to the definition of congruent figures, corresponding angles and sides are equal. Therefore, since the dimensions of congruent figures are the same, the perimeters of the figures must also be the same. This is because perimeter is a linear measure, which is the sum of the lengths of the sides of a figure.
Similarly, since congruent figures are identical in size, their areas must also be the same. Area is a measure of the extent of a 2-dimensional surface enclosed by a figure. Since the figures are congruent, they cover the same amount of 2-dimensional space, thus their areas are equal. Theorems 9 and 12 mentioned in the reference material confirm these properties.
Given: - 4x>4.
Choose the solution set.
Answer:
x < - 1
Step-by-step explanation:
Given
- 4x > 4
Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity.
x < - 1
Is this a linear f(x)= 7x^2+4
Answer:
Yes
Step-by-step explanation:
The net of a cube is shown. If the length of each edge of the cube is 5 cm, find the surface area of the cube.
Answer:
150 cm²
Step-by-step explanation:
A cube has 6 surfaces.
A cube has equal length for all edges.
Area of 1 surface = 5 x 5 = 25 cm²
Area of 6 surfaces = 25 x 6 = 150 cm²
Answer:
Step-by-step explanation:
its 600 dont belive those liers.
A line passes through the points (15,c) and (21,25) and has a slope of - 5/3
Find the value of c.
Answer: c=35
Step-by-step explanation:
to find the slope, you do y2-y1/x2-x1. So you will set up your equation like this:
25-c/21-15 = -5/3
this slope has been simplified by dividing by 2, because 21-15=6 and they simplified it to 3. So the original answer for 25-c was -10. So this means that c=35.
Find the perimeter of this shape
Answer:
4+7+3+5=19
Step-by-step explanation:
15 is 60% of what number?
Answer:
25
I don't know how to explain because I put random numbers and multiplied it by .6 and I found it once it equaled 15. Sorry I couldn't explain it more.
Claire went into a movie theater and bought 9 bags of popcorn and 2 pretzels, costing a total of $80. Melanie went into the same movie thearter and bought 7 bags of popcorn and 4 pretzels, costing a total of $72. Write a system of equations that could be used to determine the price of each bag of popcorn and the price of each pretzel. Define the variables that you use to write the system.
Answer:
9x + 2y = 807x + 4y = 72Step-by-step explanation:
Let cost of popcorns be x and pretzels be y.
Then the equations are:
9 bags of popcorn and 2 pretzels, costing a total of $80
9x + 2y = 807 bags of popcorn and 4 pretzels, costing a total of $72
7x + 4y = 72Answer:9
Step-by-step explanation:
what is 45 times 35 divided by 344
Answer:
45 times 35 = 1575 and 1575 divided by 344 = 4.578488372
Answer: 4.58
Step-by-step explanation:
45 times 35 = 1, 575
1,575/344 = 4.58 to 2 decimal place
I need help for #9 please help I got math class in 30 minutes :))!! Thank u
In questions it's given that ∠B = 85°, which is an error and correct answer is ∠B = 95°.
Step-by-step explanation:
We know that sum of alternate angles in a parallelogram is 180°. Using this property, we will solve the question! We have a parallelogram inscribed in a circle with measure of angles as ∠A=100° and ∠D=85°. Now, according to property : ∠A + ∠C = 180° and ∠D + ∠B = 180°.
Let's consider for ∠D + ∠B = 180°:
⇒ 85° + ∠B = 180°
⇒∠B = 180° - 85°
⇒∠B = 95°
Also, for ∠A + ∠C = 180°:
⇒ 100° + ∠C = 180°
⇒∠C = 180° - 100°
⇒∠C = 80°
In questions it's given that ∠B = 85°, which is an error and correct answer is ∠B = 95°.
Which of the following is the graph of y = negative 4 StartRoot x EndRoot? On a coordinate plane, an absolute value curve opens down and to the right in quadrant 1 and starts at (0, 0). On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2 and starts at (0, 0). On a coordinate plane, an absolute value curve opens up and to the right in quadrant 4 and starts at (0, 0). It goes through (5, negative 2). On a coordinate plane, an absolute value curve opens up and to the right in quadrant 4 and starts at (0, 0). It goes through (5, negative 9).
Answer:
see the procedure
Step-by-step explanation:
we have
[tex]y=-4\sqrt{x}[/tex]
we know that
The domain of a function is the set of all possible values of x
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
In this problem
The domain for x is the interval [0,∞)
All real numbers greater than or equal to zero
The range for y is the interval (-∞,0]
All real numbers less than or equal to zero
The graph in the attached figure
therefore
On a coordinate plane, an absolute value curve opens down and to the right in quadrant 4 and starts at (0, 0)
Answer:
Option C on Edge
Step-by-step explanation:
you're welcome
Solve the following systems of equations by graphing.
{
x
+
4
y
=
−
1
4
x
+
2
y
=
10
{
x+4y = -1 4x+2y = 10
Answer:
x + 4y = -1
4x + 2y = 10
-8x - 4y = -20
x + 4y = -1
-7x = -21
x = 3
3 + 4y = -1
4y = -4
y = -1
If a space shuttle traveled 36,000 miles in 5 hours how fast was it going?
Answer:7,200 mph
Step-by-step explanation:
36,000 divided by 5
Answer:
(Depends on the measurement of speed you are asking for)
7,200 Miles per hour, or 11587.28 Kilometers/hour.
Step-by-step explanation:
Divide 36,000 miles by 5 hours, and you get 7,200 per hour out of the five. Now you have the speed in miles per hour.
Hope that answered your question :)
The price per month for the Blue-tooth is $12 more than the cost for the car-phone. The sum of both items is $58. Find the cost of the Blue-tooth and car-phone. Let x equal the cost per month of the car-phone.
Answer:
Bluetooth = $41
Car Phone = 17
Step-by-step explanation:
Answer:
the bluetooth was $35 and the carphone was $23.
Step-by-step explanation:
as a salesperson, jonathan is paid $50 per week of the total amount he sells. this week, he wants to earn at least $100. write an inequality with integer coefficients for the total sales needed to earn at least $100 and describe with a solution represents
Answer: 1/5
Step-by-step explanation:50%50=1
100%50=0.5
A retail store offers all television sets at 80% or 80/100 of their original price if the customer buys a store membership for 100.00. If the p is the price of a television set. How much will a 1500.00 television cost
Answer: $1875
Step-by-step explanation:
If 80% of original price= $1500
Let the remaining 20% be x
Write as:
80/100 = $1500
20/100 = x
Cross multiply
0.8x = 1500 x 0.2
0.8x= 300
Divide both sides by 0.8
x = 300/0.8
x = 375
Therefore, 80% = 1500; 20% = 375
Price of $1500 TV without membership = $1,500 + $375
=$1,875
Answer:
It should be C. The expression is (p x 80/100) +10p and the cost is 1,300
Step-by-step explanation:
sorry if it’s wrong
which of the following values is a solution of 12.6 less than or equal to 3x
Answer:
x≤4.2
Step-by-step explanation:
12.6 ≤ 3x
1. Divide both sides by 3
2. 12.6÷3= 4.2
x≤4.2
What value of x makes this equation true? 13 - 4x = 1 - x
4
-4
−125
125
Answer:
x = 4
Step-by-step explanation:
Given
13 - 4x = 1 - x ( add x to both sides )
13 - 3x = 1 ( subtract 13 from both sides )
- 3x = - 12 ( divide both sides by - 3 )
x = 4
What is the answer to 5x-11=34
Answer:
x = 9Step-by-step explanation:
[tex]5x-11=34\qquad\text{add 11 to both isdes}\\\\5x-11+11=34+11\\\\5x=45\qquad\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{45}{5}\\\\x=9[/tex]
Answer:
x = 9
Add all numbers up get 45
5x = 45
divide both sides and get 9
Carrie started at the southeast corner of Franklin Park, walked north 240 yards, turned and walked west 80 yards, and then turned and walked diagonally back to where she started. What is the area of the triangle enclosed by path she walked?
The area is 9,600 square yards.
Carrie's walk forms a right-angled triangle, with the two legs being her north and west paths, and the hypotenuse being the diagonal path back to the start. To find the area of the triangle, we can apply the formula for the area of a right-angled triangle, which is (1/2) * base * height. In this case, the base is her westward walk (80 yards), and the height is her northward walk (240 yards).
Using the formula, the area equals: (1/2) * 80 yards * 240 yards, yielding an area of 9,600 square yards.
What is the radius and diameter of the following circle?
Answer:
The radius is 9 and the diameter is 18.
Step-by-step explanation:
Because the radius is half the diameter which is 18.
Answer:
the diameter is 18 cm and the radius is 9
Consider the point A = (1,3) and the line B, given by the equation y = 2x-2. Write an equation in slope intercept form of the line passing through point A and parallel to line B.
Please help!
The equation of the line in slope intercept form is [tex]y=2x+1[/tex]
Explanation:
The point A is [tex](1,3)[/tex]
The equation of line for B is given by [tex]y=2x-2[/tex]
We need to determine the equation of line in slope intercept form passing through the point A and parallel to line B.
Since, the lines of equation are parallel, their slopes are same.
Thus, the slope is [tex]m=2[/tex]
Now, let us substitute the point [tex]A(1,3)[/tex] and slope [tex]m=2[/tex] in the slope - point formula, we have,
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
[tex]y-3=2\left(x-1\right)[/tex]
[tex]y-3=2x-2\right)[/tex]
[tex]y=2x-2+3\right)[/tex]
[tex]y=2x+1[/tex]
Thus, the equation of the line in slope - intercept form is [tex]y=2x+1[/tex]
Is 8 feet 6 inches greater than 100
8 feet and 6 inches is equal to 102 inches, so yes
Answer: No. if your talking about 100 inches then 8 feet is 96 inches +6 = 102 inches so therefore 8 feet 6 inches is grater than 100 inches.