Answer:
First choice: 5x²+21x-20
Step-by-step explanation:
This is easy to answer if you realize that there is only one way an x² term can appear in the result and that is by the multiplication of 5x and x which results in 5x².
The only choice which has 5x² as a term is the first: 5x²+21x-20
However, it is important to know the FOIL method to multiply two terms together
FOIL stands for First Outer Inner Last and is a technique for multiplying two terms of the form (a+b) and (c+d)
In (a + b) (c + d),
First terms are a and c so their product is ac
Outer terms are a and d so their product is ad
Inner terms are b and c with product bc
Last terms are b and d with product bd
The result is the sum of all these terms
Let's take (5x - 4)(x + 5)
F: 5x·x = 5x²
O: 5x · 5 = 25x
I: -4 ·x = -4x
L: -4·5 = -20
Adding up these individual terms we get
5x² +25x - 4x - 20 = 5x²+21x-20
So first choice is the correct answer
SEE IMAGE!!! PLS HELP ASAPPP
Find the quotient. If possible, rename the quotient as a mixed number. Select the answer that is in simplest form.
3 5
8 ÷ 4 = ?
A.
1 5
8
B.
29
32
C.
25
32
Answer: B
Step-by-step explanation:
[tex]3 \frac{5}{8} \div 4=\frac{29}{8} \div 4=\frac{29}{32}[/tex]
Explain why 96:38 is NOT the same as 38:96.
The two ratios are inverse of each other that's why 96:38 is not the same as 38:96.
What are inverse ratios?When two quantities are inversely related, that is, when an increase in one quantity causes a decrease in the other and vice versa, they are said to be in inverse proportion. The product of the given two quantities is equal to a constant value in inverse proportion.
Given that the two ratios are 96:38 and 38:96. The value of the two ratios will not be the same because both the ratios are inverse of each other or are reciprocals of each other.
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Answer:
The two ratios are inverse of each other that's why 96:38 is not the same as 38:96.
Step-by-step explanation:
I took the quiz.
the inside of a flashlight surrounding the bulb is shaped like a parabola in which the base of the bulb represents the vertex and the top of the bulb represents the focus. which of the following standard equations represents the parabola in which the base of the bulb is at (1, 5) and top of the bulb is at (1, 1)? (x 1)2
The equation for the parabola is: (x - 1)^2 = 4(y - 5). The vertex of the parabola is located at (1, 5) and the focus is at (1, 1). The equation describes a parabola that opens upward, and is symmetrical about the y-axis.
The equation for the parabola is: (x - 1)^2 = 4(y - 5). This equation describes a parabola with its vertex located at (1, 5) and its focus at (1, 1). The parabola is symmetrical about the y-axis and opens upward. This means that the base of the bulb is at (1, 5) and the top of the bulb is at (1, 1). To get the equation for the parabola, we need to subtract the x-coordinate of the vertex from the x-coordinate of the focus, which gives us 1. We then square this number, giving us 1. We then subtract the y-coordinate of the vertex from the y-coordinate of the focus, giving us 4. We then multiply this number by the squared number from before, giving us 4. The final equation is then (x - 1)^2 = 4(y - 5).
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Determine if the following
lengths below will create a triangle
(3,4,5)
(10, 20, 30)
(15.5, 45, 20.5)
a. (3, 4, 5) will create a triangle.
b. (10, 20, 30) will not create a triangle
c. (15.5, 45, 20.5) will not create a triangle.
What is a triangle?
A triangle is a polygon with three sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified by their sides (such as equilateral, isosceles, or scalene) or by their angles (such as acute, right, or obtuse).
The set of lengths (3,4,5) will create a triangle. This is because it follows the "triangle inequality theorem" which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
The set of lengths (10, 20, 30) will not create a triangle. This is because 10 + 20 is less than 30, so it does not satisfy the triangle inequality theorem.
The set of lengths (15.5, 45, 20.5) will not create a triangle. This is because 15.5 + 20.5 is less than 45, so it does not satisfy the triangle inequality theorem.
Hence,
a. (3, 4, 5) will create a triangle.
b. (10, 20, 30) will not create a triangle
c. (15.5, 45, 20.5) will not create a triangle.
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Write the other side of this equation so it’a true for no values of x: 1/2(6x - 10) -x =
Answer:
2x + 3
Step-by-step explanation:
1/2(6x - 10) - x
3x -5 -x
2x -5
We would need the structure of the equation to be 2x plus or minus anything other than 15.
For example:
2x - 5 = 2x + 3 if we subtract 2x from both sides we are left with
-5 = 3 This is a false statement and their will be no solution.
How many different committees can be formed from 11 teachers and 50 students if the committee consists of 2 teachers and 2 students?
Answer:
5 committees can be formed
Step-by-step explanation:
number of teachers=11
number of students=50
number of teachers in a committee=2
number of students in a committee=2
please i need HELPPP
Answer:
vertex point is (4,-6)
and it opens upwards as the coefficient of x is positive.
I assume B is the correct answer, good luck!
Find the dot product of m=−4i−j and n=5j.
Dave has inherited an apple orchard on which 70 trees are planted. Under these conditions, each tree yields 10 bushels of apples. According to the local WSU extension agent, each time Dave removes a tree the yield per tree will go up 0.45 bushels. Let x be the number of trees in the orchard and N the yield per tree. (a) Find a formula for N in terms of the unknown x. (Hint: Make a table of data with one column representing various values of x and the other column the corresponding values of N. After you complete the first few rows of the table, you need to discover the pattern.) 41.5 – 0.45x x (b) What possible reason(s) might explain why the yield goes up when you remove trees? removing trees will mean that you will be able to share more nutrients for the trees that are left, which produces more apples per tree, and better quality of the apples as well. The yield increases as the quality and care increases for the trees.
X = 88.1. The total of all interest, dividends, or other income that an investment provides divided by the age of the investment or the period over which the investor has held it is the average yield on an investment.
What is average yield?
The average yield on an investment or a portfolio is calculated by dividing the total interest, dividends, or other income received by an investment by the investment's age or the period over which the investor has held it. In particular, it alludes to yield, or the total revenue from an investment divided by the number of years kept.
There are numerous yield kinds, and the calculating process varies depending on the specific yield type and the type of security. Because of these variations, comparisons of yields between other financial product categories should be used with caution.
In the case of stocks, yield is determined by dividing the price rise plus dividends by the original purchase price. Both cost yield and current yield can be used to examine bond yield.
Given data :
Let x be the number of trees in the orchard and N the yield per tree.
No of trees = 70
yield = 10
formula for N in terms of the unknown x :
(10+(70-x)0.55)
10 + 38.5 - 0.55x
-0.55x = 48.5
x = 48.5/ 0.55 = 88.1
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I need help with this
The point (2, 48) means in this context: Cesar and Camden are both 48 kilometers away from home after 2 hours.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Cesar and Camden are brothers and live at the same house.
Cesar is 80 kilometers away from home and bikes towards home at a rate of 16 kilometers per hour.
Camden is 20 kilometers away from home and keeps walking away from home at a rate of 14 kilometers per hour.
You found that the point of intersection on the graph is (2, 48),
and you solved algebraically to find that x=2 and y = 48.
Cesar and Camden are both 48 kilometers away from home after 2 hours.
Therefore, Cesar and Camden are both 48 kilometers away from home after 2 hours.
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What is the size, in degrees, of the missing angle?
45°
65%
The measure of the missing angle in a triangle is C = 18°.
What is a 45-Degree Angle?An acute angle is one that is 45 degrees. It is a 90-degree angle or half of a right angle. Look at the illustration of the 45-degree angle. Angles are expressed in degrees or radians.
A straight angle is one in which the two arms extend in precise opposition to one another. A 180° angle is a straight angle. A protractor can be used to measure angles; a straight angle is an angle that is measured at 90 degrees.
The two arms are perpendicular to one another at a right angle. Each angle measures 45° when the right angle is divided into two equal pieces. An acute angle is one that is 45 degrees. It is a 90-degree angle or half of a right angle.
Given one of the angles A = 45°
And B is 65% of the total angle sum = 65/100 × 180
= 117°
For angle C, using angle sum property
⇒ A + B + C = 180°
⇒ 45° + 117° + C = 180°
⇒ C = 180° - (45° + 117°)
⇒ C = 180° - 162°
⇒ C = 18°
Thus, The measure of the missing angle in a triangle is C = 18°.
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Complete question:
What is the size, in degrees, of the missing angle of a triangle?
A = 45°
B = 65%
C = x
Determine the angle between the diagonal of a cube and its edge, as shown in the figure. (Round your answer to one decimal place.)
the angle between the diagonal of a cube and its edge is equal to 35.2 degrees.
Let us consider a cube with side length = a.
Length of diagonal of cube on one of its faces = a√2
Length of diagonal of cube = a√3
To find the angle between the, use law of cosines.
The law of cosines is given by.
⇒ [tex]c^2=a^2+b^2-2abcosC[/tex]
Where c = length of side c, b = length of side b, a = length of side a
C = angle opposite to c
⇒ [tex]c^2=(a\sqrt{2})^2+(a\sqrt{3})^2-2a\sqrt{2}a\sqrt{3}[/tex]
On simplification,
[tex]cosC=\frac{2a^2}{a^2\sqrt{2}\sqrt{3}} \\cosC=\sqrt\frac{2}{3} \\[/tex]
C=35.2 degree
Therefore, the angle between the diagonals is 35.2°
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Write a two-column proof
given AX = DX, XB=XC
prove AC = BD
please help, this is for my midterm
In the parallelogram ABCD it is proved that AC ≅ BD, which proves that AC = BD.
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
It is given that the parallelogram is ABCD.
In this parallelogram AX ≅ DX, XB ≅ XC.
Now, according to the properties of parallelogram the segment addition can be done.
AC = AX + XC
Similarly, the segment addition for line BD is -
BD = DX + BX
Now if AX ≅ DX and XB ≅ XC, then substitution of DX and XC can be done -
AC = AX + BX
BD = AX + BX
This proves that AC = BD by the transitive or substitution method.
Therefore, it is proved that AC = BD and also that AC ≅ BD.
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Find the least common denominator of 1/2x-6 and 2x/7x-21.
The least common denominator to both fraction expressions is; (x - 3)
How to find the least common denominator?The least common denominator simply means the least number or expression that is common to both denominators of a given fraction.
Now, the given denominators of the fraction expression are;
(2x - 6) and (7x - 21)
To find the least common denominator here, we will just factoriuze each algebraic expression to getl
(2x - 6) = 2(x - 3)
(7x - 21) = 7(x - 3)
Thus, we see that the common expression is (x - 3) which we will conclude will be the least common denominator
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a wall 10 m long 1m high and 1/2 m wide is to be made of bricks . The bricks are of size 10 multiply 10 multiply 20 . how many bricks will be needed to make the wall.
To find out how many bricks are needed to make the wall, we need to find the total area of the wall and divide it by the area of one brick.
The area of the wall is:
length x height x width = 10 m x 1 m x 0.5 m = 5 m^2
The area of one brick is:
10 cm x 10 cm x 20 cm = 2000 cm^3
To convert the area of the wall from square meter to cubic centimeter, we need to multiply it by 100*100 = 10000.
5 m^2 x 10000 = 50000 cm^2
Now we can divide the total area of the wall by the area of one brick to find out how many bricks are needed:
50000 cm^2 / 2000 cm^2/ brick = 25 bricks
So, 25 bricks will be needed to make the wall.
Solve for x
8√3
12.
Select the correct response:
8
16
15
4√3
X
Answer:
see below & attached
Step-by-step explanation:
red line length call it a² = (8√3)²- 12² = 192-144 =48
so look at the graph we know x is longer than 12,
the portion that's longer than 12 call it c = x-12
top short line call it b
because it's all right angle you are looking at 3 right angle triangles
the big one that's cut into 2 by the red line
the larger one & the smaller one
each will have this property: short side 1 ²+short side 2 ²= long side ²
so for the largest one:
(8√3)² +b² = (12+c)² = x²
second largest triangle we already know all 3 sides: (8√3), 12, √48
now look at the smallest
48+c² =b²
once you have all equations listed , you can solve for c.
see attached.
Nick selects a simple random sample of 25 seniors at his large school and finds that 20 of them eat a healthy breakfast. He wants to construct a confidence interval for p = the proportion of all seniors at this school who eat a healthy breakfast, but he realizes he hasn't met all the conditions for constructing the interval. Which condition for this procedure has he failed to meet?
n ≥ 30
n p hat greater-than-or-equal-to 10
n (1 minus p hat) greater-than-or-equal-to 10
The sample size must be less than 10% of the population size.
Nick has failed to meet the condition that n p hat greater-than-or-equal-to 10 and n (1 minus p hat) greater-than-or-equal-to 10.
In order for the Central Limit Theorem to be applied and for the sample proportion to be approximately normally distributed, the sample size must be at least 30. This means that the sample size must be large enough so that the sample proportion of healthy breakfast eaters (p hat) and the sample proportion of non-healthy breakfast eaters (1-p hat) are both greater than or equal to 10. In this case, since the sample proportion of healthy breakfast eaters is 20/25 = 0.8, the sample proportion of non-healthy breakfast eaters is 5/25 = 0.2. Since 5 is less than 10, this condition is not met, and Nick cannot construct a confidence interval for p.
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5+w=8 simplified in to simplest form
[tex] \large \frak{ \green 5 + \red{w }= \green 8}[/tex]
[tex] \: [/tex]
[tex] \ \: \large \frak{ \red{w }= \green 8 { -} \green5}[/tex]
[tex] \: [/tex]
[tex] \underline{ \boxed{ \large \frak{ \: \red{w }= \green 3 \: }}}[/tex]
[tex] \: [/tex]
hope it helps!
Si mi tía llega a la casa con cuatro donas de azúcar y estamos seis personas en la casa ¿ de cuánto nos tocaría ha cada uno en fracciones?
A coda ulna de las personas le Toccara ulna porcino de 2/3 de Dona
de canto no's Toccara ha coda uno eon fractions?Si mi tía ha legato a la casa y trae consigo 4 Donas de azúcar, pero no se ha percatado que la cantidad de personas en la casa es de 6 contándose, entonces decide repartir en partes iguales, para esta operation deems divider la candida de donnas entre la cantidad de personas
4 donnas / 6 personas = 2 /3 ester 2/3 es la porcino de coda uno es décor coda Dona se picara eon tress torsos y dos torsos para coda persona de 2/3
Respuesta:
para que alkanes les tocaria
a 4 personas la mated de una dona
(osea 2 donas las partes a la mated)
y a las okras 2 personas la Dona entera
Explication paso a paso:
esparto hiver aoudad:)
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Can you help me with this question its times
The length of side LN is equal to 44 units. (Correct choice: A)
How to determine a missing length in a system of two similar trianglesTwo triangles are similar when these triangles have congruent angles but non-congruent though proportional sides. Triangles LMN and NUV are similar. Therefore, we can determine the length of side LN of geometrical system by means of following relationship:
NV / LN = NU / MN
LN = NV × MN / NU
If we know that NV = 11, MN = 32 and NU = 8, then the length of side LN is:
LN = 11 × (32 / 8)
LN = 11 × 4
LN = 44
The side LN has a length of 44 units.
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Kerri keeps a bowl of change on her dresser. She only keeps dimes and quarters. She has five dollars in change in the bowl right now. If she has exactly 29 coins in the bowl, how many quarters does she have?
The number of quarters in the bowl is 14.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x+ 3 = 9 is an equation.
We have,
Dimes = x
Quarters = y
10 dimes = $1
1 dime = $0.1
4 quarters = $1
1 quarter = $0.25
Now,
0.1x + 0.25y = 5 _____(1)
x + y = 29 _____(2)
Solve for y from (1) and (2),
x = 29 - y
Substitute in (1) we get,
0.1 (29 - y) + 0.25y = 5
2.9 - 0.1y + 0.25y = 5
2.9 + 0.15y = 5
0.15y = 5 - 2.9
y = 2.1/0.15
y = 14
Thus,
There are 14 quarters in the bowl.
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The sum of four consecutive odd integers is 264. Find the integers.
The smallest of the four consecutive integers is?
Answer:
63
Step-by-step explanation:
Consecutive odd integers increase by the addition of 2 therefore if the smallest value is x then the next odd number is x + 2
So therefore; x + x + 2 + x + 4 + x + 6 = 264
Collect like terms
x + x + x + x + 2 + 4 + 6 = 264
4x + 12 = 264
4x = 264 - 12
4x = 252
Divide both sides by 4
x = 63
Therefore the smallest of the four consecutive integers is 63
construct the general solution of involving complex eigenfunctions and then obtain the general real solution. describe the shapes of typical trajectories.
The ODE's general solution has real solution and complex eigen functions. Typical trajectories are sinusoidal curves.
The general solution of the ODE involves complex eigenfunctions, which are solutions of the form e^(ikx), where k is a real number and i is the imaginary unit. By combining these complex eigenfunctions with real coefficients, a general real solution can be obtained. Typically, these solutions will take the form of sinusoidal curves, with the amplitude and period determined by the coefficients of the eigenfunctions. The coefficients can be determined using initial conditions, allowing for more specific trajectories to be determined. For example, if the initial condition is known, then the coefficients of the eigenfunctions can be determined using Fourier analysis, allowing for the trajectory of the system to be determined.
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A rancher wants to enclose a rectangular field with 220 ft of fencing. One side is a river and will not require a fence. What is the maximum area that can be enclosed?
5329 Sq meters is the maximum area that can be enclosed.
What is a rectangle, exactly?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. It is also known as an equiangular quadrilateral for this reason.
The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
Perimeter of Rectangle: 2W + 2L
One L is the river so we have 3 sides
220m/3 = 73m
Area of Rectangle is WL
73 × 73 = 5329 Sq meters
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7-89. For angle α in the first quadrant, . Use that information to find each of the
following values without using a calculator. Be prepared to share your strategies with the class.
a. sin α
b. sin(π + α)
c. cos(2π − α)
The required values are for the given angle, as follows: a. sin α is positive. b. sin(π + α) = -sin α. c. cos(2π - α) = cos α.
What is the quadrant?A quadrant is defined as an area contained by the x and y axes, which there are four quadrants in a graph.
a. For an angle α in the first quadrant, sin α is positive.
Since the first quadrant is between 0 and 90 degrees, sin α is equal to the opposite side divided by the hypotenuse, where the opposite side is the y-coordinate and the hypotenuse is the distance from the origin to the point on the unit circle corresponding to the angle α.
b. sin(π + α) = sin (π - α). In the second quadrant (90 < α < 180), sine is negative, so sin(π + α) = -sin α.
c. cos(2π - α) = cos α. The cosine function has period 2π, so cos(2π - α) = cos α.
Since the first quadrant is between 0 and 90 degrees, cos α is positive.
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Marie earns £340 each week.She is given a 6.5% pay rise. How much does she earn each week after the pay rise?
Answer:
£362.1
Step-by-step explanation:
6.5% =
6.5 / 100 =
65 / 1000 = 0.065
£340 * 0.065 = £22.1 => £22.1 is the pay raise in terms of English pounds(£)
Now add the pay raise to the earnings per week to get the total earnings after the raise:
£22.1 + £340 =
£22.1 + £340.0 = £362.1
two sides of a triangle are 19.75 and 10.25. select all choices that could represent the third side of the triangle.
the two possible values for the third side of the triangle are 22.5 and 24.00.
We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, the third side must be greater than 10.25 and less than 19.75.
From this, we can conclude that the third side of the triangle must be either 22.5 or 24.00.
We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given that two sides of the triangle measure 19.75 and 10.25, the third side must be greater than 10.25 and less than 19.75. Therefore, the only two possible lengths for the third side of the triangle are 22.5 and 24.00. Any length greater than 19.75 or less than 10.25 would not satisfy the triangle inequality and would not be a valid third side for the triangle. Thus, We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
the two possible values for the third side of the triangle are 22.5 and 24.00.
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i need help with the following question below
Answer:
see below
Step-by-step explanation:
b = √3
then move t to the end you'll see
m= -0.4√13
An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in
x = 18.19 kgf/cm2 for the modified mortar (m = 42) and y = 16.87 kgf/cm2 for the unmodified mortar (n = 32). Let m1 and m2 be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal.
(a) Assuming that ?1 = 1.6 and ?2 = 1.3, testH0: m1 ? m2 = 0 versus Ha: m1 ? m2 > 0 at level 0.01.
State the rejection region(s). (If the critical region is one-sided, enter NONE for the unused region. Round your answers to two decimal places.)
z ? z ? Compute the test statistic value. (Round your answer to two decimal places.)
z = State the conclusion in the problem context.
Reject H0. The data does not suggest that the difference in average tension bond strengths exceeds 0.
Fail to reject H0. The data does not suggest that the difference in average tension bond strengths exceeds from 0.
Fail to reject H0. The data suggests that the difference in average tension bond strengths exceeds 0.
Reject H0. The data suggests that the difference in average tension bond strengths exceeds 0.
the data suggests that the difference in average tension bond strengths is greater than 0. In other words, the polymer latex modified mortar has a higher tension bond strength than the unmodified mortar.
a) The rejection region for this one-tailed hypothesis test is z ? z > 2.33.
The test statistic value is z = 2.76.
Therefore, the conclusion is that we reject H0. The data suggests that the difference in average tension bond strengths is greater than 0.
For this one-tailed hypothesis test, we must reject the null hypothesis (H0: m1 - m2 = 0) if the test statistic is greater than 2.33. Our test statistic value is 2.76, which is greater than 2.33, so we reject H0. This indicates that the data suggests that the difference in average tension bond strengths is greater than 0. In other words, the polymer latex modified mortar has a higher tension bond strength than the unmodified mortar.
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Draw a triangle with a side length of 1 1/4 inches and a side length of 1 3/4 inches that meet at a 50 degree angle.
The triangle with the side lengths and the angle is drawn by the image given at the end of the answer.
The area of the triangle is given as follows:
1.68 inches squared.
How to obtain the area of a triangle?The area of a triangle, given two side lengths a and b, and the angle θ between them, is given as follows:
A = ab x sin(θ).
The parameters for this problem are given as follows:
a = 1.25, as 1/4 = 0.25.b = 1.75, as 3/4 = 0.75.The angle is of 50º, hence the area is given as follows:
A = 1.25 x 1.75 x sin(50º)
A = 1.68 inches squared.
Missing InformationThe problem asks for the area of the triangle.
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