Answer:
Approach: Difference of Squares Pattern
[tex]4 {x}^{2} - 25 = (2x - 5)(2x + 5)[/tex]
Step-by-step explanation:
The given binomial is:
[tex]4 {x}^{2} - 25[/tex]
We can rewrite to obtain:
[tex] {(2x)}^{2} - {5}^{2} [/tex]
This is a difference of two squares, so we will factor using difference of squares pattern.
Recall that:
[tex] {a}^{2} - {b}^{2} = (a + b)(a - )[/tex]
If we let
[tex]a = 2x[/tex]
and
[tex]b = 5[/tex]
Then we can factor the given binomial to obtain:
[tex] {2x}^2 - {5}^{2} = (2x - 5)(2x + 5)[/tex]
[tex] \therefore4 {x}^{2} - 25 = (2x - 5)(2x + 5)[/tex]
Find the value of x in the triangle shown below.
x =
In the triangle it has 74, 20, and x degrees
Answer:
86
Step-by-step explanation:
Angles in a triangle add up to 180 degrees
add 74 with 20 to get 94
subtract 94 from 180 to get the value of x
180-94=86
The value of x in the triangle whose two interior angle values are given as 74 degrees and 20 degrees is 86 degrees.
What is a triangle?A triangle is a closed 2-dimensional polygon with three angles and three straight sides.
According to the Triangle Angle Sum Theorem, the sum of the three interior angles in a triangle is always 180°.
Hence,
angleA + angleB + angleC = 180°
Given the data in the question;
First angle in the triangle A = 74°Second angle in the triangle B = 20°Third angle in the triangle C = xWe substitute our given values into the expression above.
angleA + angleB + angleC = 180°
74° + 20° + x = 180°
94° + x = 180°
x = 180° - 94°
x = 86°
Hence, the value of x in the triangle whose two interior angle values are given as 74 degrees and 20 degrees is 86 degrees.
Learn more about polygons here: https://brainly.com/question/12729233
#SPJ2
By graphing both sides of the equation, determine whether the following is an identity:
1+sec^2x= tan^2 x
Graphing is overkill... Let [tex]x=0[/tex]. Then [tex]\sec0=1[/tex], while [tex]\tan0=0[/tex]. But [tex]1+1=2\neq0[/tex], so this is not an identity.
Answer:
It is not an identity
Step-by-step explanation:
If you graphic the two equations (left and right) separately, if they are an identity, they will be the same graphic, which is not true in this case.
Another way in order to know if an equation is an identity, you can replace some values at x, for example 2 values:
X=30
X=60
And now we substitute in the equation, like this:
[tex]1+sec^2(30)=tan^2(30)[/tex]
2,33=0,33 this is not equal on both sides
[tex]1+sec^2(60)=tan^2(60)[/tex]
5=3 this is not equal on both sides
And if the results for each number x are the same on both sides of the equation, it is an identity. In this case they are different.
A rectangle measures 3 inches by 4 inches. If the lengths of each side double,what will its area be
6x8= 48 inches
3 doubled=6
4 doubled=8
Point W is located at (-2,3) on a coordinate plane. Point W is reflected over the x-axis to create point w'. Point W' is then reflected over the y-axis to create point W". What ordered pair describes the point location of point W"?
ANSWER
[tex]W''(2, - 3)[/tex]
EXPLANATION
The given point bas coordinates
W(-2,3).
The mapping for reflection over the x-axis is
[tex](x,y)\to(x, - y)[/tex]
[tex]W(-2,3)\to \: W'(-2, - 3)[/tex]
This point W'(-2,-3) is then reflected over the y-axis.
The mapping for reflection over the y-axis is
[tex](x,y)\to (-x, y)[/tex]
[tex]W'(-2,-3)\to \: W''(2, - 3)[/tex]
Point W is initially transformed by reflecting it over the x-axis, which inverses the sign of the y-coordinate, followed by a reflection over the y-axis, which inverses the sign of the x-coordinate. The final position of point W" on the coordinate plane is therefore (2, -3).
Explanation:To answer this mathematics question involving coordinate geometry and reflections, one must understand how reflections in the x-axis and y-axis affect the coordinates of a point.
A reflection of a point across the x-axis changes the sign of the y-coordinate, and a reflection across the y-axis changes the sign of the x-coordinate. Thus, if we start with point W at (-2,3), a reflection over the x-axis to create point W' changes the y-coordinate's sign, yielding point W' at (-2,-3). Then, reflecting W' over the y-axis changes the x-coordinate's sign, yielding our final point W" at (2,-3).
Learn more about Coordinate Geometry here:https://brainly.com/question/29886206
#SPJ3
Adrianna has fabric that is 34 yard long. She needs to cut the fabric into pieces that are 18 yard long. How many 18 -yard-long pieces will she have?
Question 4 options:
6
7
8
9
(Will give brainliest- please explain)
Answer:
2
Step-by-step explanation:
Dividing 18 yds into 34 yds yields 2; Adrianna will have 2 pieces 18 yds long, with 8 yds left over.
A rectangular prism is 3 inches long, 5 inches wide, and has a height of 6 inches. What is its surface area?
a.63 in2
b. 90 in2
c.120 in2
d.126 in2
Answer:
the answer is D.126
Step-by-step explanation:
Use the formula A=2(wl+hl+hw)
A trough is filled with water. The trough holds 315 gallons. Each cubic foot of water contains about 7.5 gallons. The trough is 7 feet long and 4 feet wide. What is the height of the trough?
Answer:
The height of the trough is about 1.5 ft
Step-by-step explanation:
If each cubic foot of water contains about 7.5 gallons.
Then; 315 gallons is about [tex]\frac{315}{7.5}=42ft^3[/tex]
Let h be the height of the trough, then
[tex]7\times 4\times h=42[/tex]
This implies that;
[tex]28h=42[/tex]
Divide both sides by 28 to get:
[tex]h=\frac{42}{28}[/tex]
[tex]\therefore h=1.5[/tex]
The height of the trough is about 1.5 ft
the height of the trough is 1.5 feet.
To solve for the height of the trough that holds 315 gallons, we need to use the information that 1 cubic foot of water contains about 7.5 gallons. Since the trough is 7 feet long and 4 feet wide, we can first calculate the volume in cubic feet by dividing the volume in gallons by the gallon-to-cubic-feet conversion factor (315 gallons \/ 7.5 gallons/cubic foot). Then, we use this volume to find the height by dividing the volume by the product of the length and the width of the trough.
Here is a step-by-step approach:
Convert the volume from gallons to cubic feet: Volume (cubic feet) = Volume (gallons) ÷ 7.5 gallons/cubic footCalculate the height of the trough: Height (feet) = Volume (cubic feet) ÷ (Length (feet) x Width (feet))Now, let's calculate:
Volume (cubic feet) = 315 gallons ÷ 7.5 gallons/cubic foot = 42 cubic feetHeight (feet) = 42 cubic feet ÷ (7 feet x 4 feet) = 42 cubic feet ÷ 28 square feet = 1.5 feetTherefore, the height of the trough is 1.5 feet.
Why do insurance companies charge more for women than men? Is that fair? Why or why not?
Answer:
because women are still commonly looked down upon, and men more superior. It is not fair due to the fact that women get paid less and men get hired for more jobs.
Step-by-step explanation:
Yasmin ran 6 2/3 miles on wednesday.On saturday she ran 2 1/4 times as far as she did on wednesday.How far did Yasmin run on saturday
For this case we have to:
Wednesday:
[tex]6 \frac {2} {3} = \frac {3 * 6 + 2} {3} = \frac {20} {3}[/tex]
Saturday:
He ran [tex]2 \frac {1} {4}[/tex] times more than on Wednesday, that is:
[tex]\frac {20} {3} + \frac {4 * 2 + 1} {4} =\\\frac {20} {3} + \frac {9} {4} =\\\frac {20 * 4 + 9 * 3} {12} =\\\frac {107} {12} =\\8 \frac {11} {12}[/tex]
Thus, on Saturday, he ran [tex]8 \frac {11} {12}[/tex]miles
Answer:
[tex]8 \frac {11} {12}[/tex]
Rewrite the following parametric equations in rectangular form.
x=e^3t and y= e^-t
a. y=3/x, x>0
b.x= 1/y^3, y>0
c. x= -y^3,y<0
d. y= 1/x^3, x>0
Answer:
Answer choice B
Step-by-step explanation:
What is the surface area of the rectangular pyramid below
[tex]S=15\times15+4(7.5\times15)=\boxed{675}[/tex]
Answer:
Option C is correct.
Step-by-step explanation:
Given:
Length of the base rectangle = 15 unit
Width of the base rectangle = 15 unit
Height of triangle on the side of pyramid = 15 unit
Length of the base of the triangle = 15 unit
Surface are of the rectangular pyramid = Area of Base + 4 × Area of triangle on side.
Area of base = length × width = 15 × 15 = 225 unit²
Area of the triangle = 1/2 × base × height = 1/2 × 15 × 15 = 112.5 unit²
Surface Area = 225 + 4 × 112.5 = 225 + 450 = 675 unit²
Therefore, Option C is correct.
Use the partial information given in this electronic W-2 form to calculate the amount in Box 3.
The Box 3 on an electronic W-2 form represents the total wages subject to Social Security tax. To calculate it, look for the 'Social Security wages' value on the form and determine if it exceeds the annual limit set by the Social Security tax.
Explanation:The Box 3 on an electronic W-2 form represents the total wages that are subject to the Social Security tax. To calculate the amount in Box 3, you can look for the value labeled 'Social Security wages' or 'SS wages' on the form. This value includes all taxable wages and tips that are subject to Social Security taxes, up to a certain limit.
For the year 2020, the Social Security tax is only applied to the first $137,700 of wages. If the 'Social Security wages' value provided on the form is higher than this limit, you should use the limit as the amount in Box 3. If the value is lower than the limit, then the 'Social Security wages' value itself should be used as the amount in Box 3.
Learn more about box 3 on electronic W-2 form here:https://brainly.com/question/31891188
#SPJ2
Three scatterplots are shown, along with their best-fit lines and correlation coefficients, r1, r2, and r3. Choose the correct statement.
A) r1 < r2 < r3
B) r2 < r1 < r3
C) r3 < r2 < r1
D) r1 < r3 < r2
Answer:
C) r3 < r2 < r1
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
16. What are the values of a and b?
Answer:
a = 20; b = 2√101
Step-by-step explanation:
The triangle at upper left and the one at lower right are similar. Ratios of corresponding sides are equal, so ...
200/a = a/2
400 = a^2
√400 = 20 = a
Then, by the Pythagorean theorem, the value of b can be found:
b = √(a^2 + 2^2) = √(400 +4) = √4·√101
b = 2√101
HELP PLEASE!!!
What is the solution to the system of equations below?
y=1/2x-4 and y=-2x-9
A) (-2,-5)
B) (-2,-3)
C) (2, -3)
D (2,-13)
PLEASE HELP THANKS!!
Answer:
(-2,-5)
Step-by-step explanation:
y=1/2x-4 and y=-2x-9
Just substitute one into the other and then solve for x. Then go back to get y.
1/2x-4=-2x-9
Add 4 on both sides
1/2x =-2x-5
Add 2x on both sides
2.5x=-5
Divide both sides by 2.5
x=-5/(2.5)=-2
Plug into y=-2x-9 to find y.
y=-2(-2)-9=4-9=-5.
Answer (-2,-5)
Answer:
A) (-2,-5)
Step-by-step explanation:
a parabola is the set of all points that:
Answer:
Option C.
Step-by-step explanation:
Option C. A parabola is a set of all points that are the same distance from a point called focus and a line called vertex.
The correct option is option C.
A parabola is a set of all points that are the same distance from a point called focus and a line called vertex.
The parabola is symmetric about its axis.
Learn more about parabola here:
https://brainly.com/question/11911877
#SPJ6
A small dog gets fed 3/4 cups of dog food twice a day. Using d for the number of days and f for the amount of dog food in cups, write an equation relating the variables. Use the equation to find how many days a large bag of dog food will last if it contains 210 cups of food?
The desired equation relating the variables is;
d = 4f/6Also, a large bag of dog food that contains 210 cups of food will last 140 days according to the equation.
According to the question;
The small dog gets fed 3/4 cups of dog food twice a day.
In essence; The dog is fed twice a day with 3/4 cups of dog food each time.
Therefore; The dog gets fed 2× (3/4) cups of dog food per day
a) The equation is therefore;
d = f/(6/4)d = 4f/6.b) To determine the number of days a large bag of dog food will last if it contains 210 cups of food;
d = 4f/6d = (4 × 210)/6d = 140 daysRead more:
https://brainly.com/question/3796978
This is the graph of f(x)=4(1/2)^x. What is the horizontal asymptote of f(x)?
ANSWER
The correct choice is D.
EXPLANATION
See the attachment for explanation;
Write an equation for that graph,where y depends on x.
____
To create an equation for a graph where y depends on x, identify the type of relationship presented by the graph. For a linear relationship, use the formula y = mx + b, where 'm' is the slope and 'b' is the y-intercept. Determine the slope using two points on the line and then solve for 'b' using the slope and one of the points.
Explanation:Creating an equation for a graph where y depends on x is a common task in algebra. It's essential to identify the type of relation presented by the graph, which may include linear, quadratic, exponential, or logarithmic relationships. Let's assume, for example, that the graph represents a simple linear relationship.
In this case, you would use the formula for a line, which is y = mx + b. 'm' represents the slope of the line, and 'b' stands for the y-intercept.
To find the slope 'm', you can choose two points on the line and calculate the change in y divided by the change in x. Once the slope is determined, plug one of the points' coordinates into the equation and solve for 'b', the y-intercept. This will give you the equation for the line.
Learn more about Equation of Graph here:https://brainly.com/question/35277826
#SPJ2
The equation for that graph, where y depends on x can be expressed in slope-intercept form as: y = -2x + 6.
What is the equation of a linear graph?To find the equation of the line, you can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. First, find the slope (m) using any two given points on the graph, i.e. (0, 6) and (4, -2):
[tex]\[ m = \frac{{\text{{change in }} y}}{{\text{{change in }} x}} = \frac{{-2 - 6}}{{4 - 0}} = \frac{{-8}}{{4}} = -2 \][/tex]
Now, substitute one of the points (e.g., (0, 6)) and the slope into the equation:
y = mx + b
6 = -2(0) + b
b = 6
So, the equation of the line is y = -2x + 6.
Learn more about equation of a line on:
https://brainly.com/question/18831322
#SPJ2
Please help me with this!!
Thank u
Answer:
Step-by-step explanation:
Left
When a square = a linear, always expand the squared expression.
x^2 - 2x + 1 = 3x - 5 Subtract 3x from both sides
x^2 - 2x - 3x + 1 = -5
x^2 - 5x +1 = - 5 Add 5 to both sides
x^2 - 5x + 1 + 5 = -5 + 5
x^2 - 5x + 6 = 0
This factors
(x - 2)(x - 3)
So one solution is x = 2 and the other is x = 3
Second from the Left
i = sqrt(-1)
i^2 = - 1
i^4 = (i^2)(i^2)
i^4 = - 1 * -1
i^4 = 1
16(i^4) - 8(i^2) + 4
16(1) - 8(-1) + 4
16 + 8 + 4
28
Second from the Right
This one is rather long. I'll get you the equations, you can solve for a and b. Maybe not as long as I think.
12 = 8a + b
17 = 12a + b Subtract
-5 = - 4a
a = - 5/-4 = 1.25
12 = 8*1.25 + b
12 = 10 + b
b = 12 - 10
b = 2
Now they want a + b
a + b = 1.25 + 2 = 3.25
Right
One of the ways to do this is to take out the common factor. You could also expand the square and remove the brackets of (2x - 2). Both will give you the same answer. I think expansion might be easier for you to understand, but the common factor method is shorter.
(2x - 2)^2 = 4x^2 - 8x + 4
4x^2 - 8x + 4 - 2x + 2
4x^2 - 10x + 6 The problem is factoring since neither of the first two equations work.
(2x - 2)(2x - 3) This is correct.
So the answer is D
What is this equal to?
ANSWER
[tex] \sum_{n=1} ^{32} (4n + 1) = 2144[/tex]
EXPLANATION
The given series is
[tex] \sum_{n=1} ^{32} (4n + 1) [/tex]
The first term in this series is
[tex]a_1=4(1) + 1 = 5[/tex]
The last term is
[tex]l = 4(32) + 1 = 129[/tex]
The sum of the first n terms is
[tex]S_n= \frac{n}{2} (a + l)[/tex]
The sum of the first 32 terms is
[tex]S_ {32} = \frac{32}{2} (5 + 129)[/tex]
[tex]S_ {32} =16 \times 134[/tex]
[tex]S_ {32} =2144[/tex]
Therefore,
[tex] \sum_{n=1} ^{32} (4n + 1) = 2144[/tex]
Given that lines b and c are parallel, select all that apply. Which pairs of angles are supplementary?
1 and 4
5 and 6
2 and 8
3 and 6
Supplementary angles, totaling 180 degrees, are demonstrated by ∠2 and ∠4, as well as ∠3 and ∠5, in the context of lines b and c, as depicted in the diagram.
Supplementary angles are pairs of angles whose measures add up to 180 degrees. In the context of lines b and c, the identified supplementary angle pairs are ∠2 and ∠4, as well as ∠3 and ∠5. These pairs satisfy the condition that the sum of their measures equals 180 degrees. Visually, this relationship is evident in the provided diagram, reinforcing the concept of supplementary angles. Specifically, the equation ∠2 + ∠4 = 180° and ∠3 + ∠5 = 180° illustrates the supplementary nature of these angle pairs. Understanding supplementary angles is crucial in geometry, as it provides a fundamental principle for evaluating the relationships between angles formed by intersecting lines. In the given scenario, the angles ∠2, ∠4, ∠3, and ∠5 exhibit supplementary properties, emphasizing their collective role in forming a straight line and contributing to the overall understanding of geometric configurations.
The correct question maybe :-
Given in the attachment
HELP ASAP PLEASE!!!
If f(x)=5x-1, What is f^-1 (f(2))?
A. 44
B. -2
C. -44
D. 2
Answer:
(D) 2
Step-by-step explanation:
f(x) = 5x - 1
y = 5x - 1
5x = y + 1
x = (y + 1)/5
f⁻¹ (x) = (x + 1)/5
f(x) = 5x - 1
f(2) = 5(2) - 1
f(2) = 9
f⁻¹ (x) = (x + 1)/5
f⁻¹ (f(2)) = (9 + 1)/5
f⁻¹ (f(2)) = 2
Pls answer this question
x^2 -4x +2=0
There are two options of x. You have both of them in picture 1.
Answer:
Step-by-step explanation:
x² - 4x +2=0
(x² - 4x +4) - 4+2=0
(x - 2)²= 2
x - 2 = √2 or x- 2 = -√2
x=2+√2 or x=2-√2
note : same solution :Magdaloskotova Beginner
(4+2√2)/2 = 2(2+√2)/2 = 2+√2
(4-2√2)/2 = 2(2-√2)/2 = 2-√2
The mass of a ball is 128 g. It has a density of 0.5 g/cm³.
What is the volume of the ball?
Show your work and place a box around your answer.
Answer:
The volume of the ball is 256 cm³
Step-by-step explanation:
we know that
The density is equal to the ratio of the mass by the volume
D=m/V
Solve for V
The volume is equal to the ratio of the mass by the density
V=m/D
In this problem we have
m=128 g
D=0.5 g/cm³
substitute
V=128/0.5=256 cm³
What is the phase shift and period for the function y = 3cos6(θ − 30°) + 4?
Phase shift = right 30°, period = 60°
Phase shift = right 30°, period = −60°
Phase shift = left 30°, period = 60°
Phase shift = left 40°, period = 30°
ANSWER
Phase shift = right 30°, period = 60°
EXPLANATION
See attachment.
Which describes the correct order of steps for constructing an angle bisector of ∠DEF using only a straightedge and compass?
ANSWER CHOICES IN 2ND IMAGE.
Answer:
D
Step-by-step explanation:
The following steps describes the correct order of steps for constructinf an angle bisector of angle DEF.
(1). Draw a circle with a radius less then the arms of angle.
(2). Draw a line from point of intersections of arc (circle) and arms of the angle.
(3). Draw two circles with radius = distance between point of intersection of circle and arms of angle, center taken as point of intersection of circle and arms. than draw an equilateral triangle.
(4). Use a straightedge to connect the vertex of angle and the right most vertex of the equilateral triangle.
Hence option D is correct.
Shaun's savings can be modeled by the regression equation y = 6x^2 + 75x+200. Which of the following is the best prediction for the amount he will have saved after 25 months?
A. $3,791
B. $4,754
C. $2,936
D. $5,825
Answer:
D
Step-by-step explanation:
The equation given gives y in terms of x, where y is Shaun's savings and x is the number of months.
We want to know the amount he will save in 25 months, so we can plug in x = 25 into the equation and get a value of y, that is the amount he will save. So:
[tex]y = 6x^2 + 75x+200\\y = 6(25)^2 + 75(25)+200\\y=5825[/tex]
D is the correct answer.
A die with numbers 1 through 6 is rolled. What is the probability of getting a 4 on the first roll and then getting a 4 or a 6 on the second roll?
the probability is 1/18
what is the probability of selecting a number that is a multiple of 15?
Answer:
well since there are infinite numbers the probability is hard to solve. is there like a:
what is the probability of selecting a number that is a multiple of 15 in a hat that has paper with numbers from 1- 100
kind of thing?
Step-by-step explanation: