For each game, Drew spends 10.75 minutes, this means in total Drew spends
[tex]5\cdot10.75\text{ minutes}[/tex]this product gives
[tex]5\cdot10.75=53.75\text{ minutes}[/tex]then, in the fifth challenge Drew spends 53.75 minutes
The diamond method for factoring: Fill in the missing value
Consider a quadratic expression, let "m" and "n" represent the factors.
The diamond method of factoring is the following:
On the left of the diamond, there is one of the factors, for example, "m", of the right of the diamond you will find the other factor "n".
On the top of the diamond, you will find the product of both factors, on the bottom of the diamond you will find the sum of the factors.
Looking at the given diamond, you know the result of the product and the sum of both factors:
[tex]m*n=-15[/tex][tex]m+n=14[/tex]Using these expressions, you can find both factors.
- First, write the second expression for one of the variables, for example, for "n"
[tex]\begin{gathered} m+n=14 \\ m=14-n \end{gathered}[/tex]- Second, replace the expression obtained on the second equation:
[tex]\begin{gathered} m*n=-15 \\ (14-n)n=-15 \end{gathered}[/tex]Distribute the multiplication
[tex]14n-n^2=-15[/tex]Zero the expression and order the terms from greatest to least:
[tex]\begin{gathered} 14n-n^2+15=-15+15 \\ 14n-n^2+15=0 \\ -n^2+14n+15=0 \end{gathered}[/tex]- Third, use the quadratic expression to determine the possible values of n:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Where
a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant
For the quadratic expression obtained, where "n" represents the x-variable.
[tex]-n^2+14n+15=0[/tex]The coefficients are:
a= -1
b=14
c=15
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ n=\frac{-14\pm\sqrt{14^2-4*(-1)*15}}{2*(-1)} \\ n=\frac{-14\pm\sqrt{196+60}}{-2} \\ n=\frac{-14\pm\sqrt{256}}{-2} \\ n=\frac{-14\pm16}{-2} \end{gathered}[/tex]Solve the sum and difference separately to determine both possible values for "n"
→Sum:
[tex]\begin{gathered} n=\frac{-14+16}{-2} \\ n=\frac{2}{-2} \\ n=-1 \end{gathered}[/tex]→Difference:
[tex]\begin{gathered} n=\frac{-14-16}{-2} \\ n=\frac{-30}{-2} \\ n=15 \end{gathered}[/tex]- Finally, determine the possible value/s of m:
For n=-1
[tex]\begin{gathered} m+n=14 \\ m+(-1)=14 \\ m-1=14 \\ m=14+1 \\ m=15 \end{gathered}[/tex]For n=15
[tex]\begin{gathered} m+n=14 \\ m+15=14 \\ m=14-15 \\ m=-1 \end{gathered}[/tex]So, the factors are -1 and 15 and the diamond is:
4x squared- 5x +4-(9x squared +3x -1)
hello
the question here requires the subtraction of polynomials
[tex]\begin{gathered} 4x^2-5x+4 \\ - \\ 9x^2+3x-1 \end{gathered}[/tex]if we are to do this, we have to subtract the polynomials based on their degree
this would be equal to
[tex]-5x^2-8x+5[/tex]the above polynomial is the result after subtraction, but we can as well, decide to multiply through by -1, to make or eilimate the negative sign on the second degree polynomal
[tex]\begin{gathered} (-5x^2-8x+5)\times-1 \\ = \\ 5x^2+8x-5 \end{gathered}[/tex]Identify the center and the radius of the circle.(x - 1)^2+ (y + 3) = 4
We are given the following equation of a circle.
[tex]\mleft(x-1\mright)^2+(y+3)^2=4[/tex]The standard form of the equation of a circle is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]Comparing the given equation with the standard form we see that
[tex]\begin{gathered} h=1 \\ k=-3 \\ r^2=4 \\ r=\sqrt[]{4} \\ r=2 \end{gathered}[/tex]Therefore, the center of the circle is
[tex]C=(h,k)=(1,-3)[/tex]Therefore, the radius of the circle is
[tex]r=2[/tex]The diameter of the pool is 5 feet. What is the circumference of the pool?
"∆ABC~∆DEF. The area of ∆ABC is given. Find the area of ∆DEF. Do not lable the final answer."
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
∆ABC~∆DEF
triangle 1:
AC = 10
area = 65 in²
triangle 2:
DF = 20
area = ?
Step 02:
We must apply the rules of similar triangles to find the solution. .
[tex]\frac{triangle\text{ 1 AC}}{\text{triangle 2 DF }}=\frac{triangle\text{ 1 area}}{\text{triangle 2 area}}[/tex][tex]\frac{10}{20}=\frac{65in^2}{triangle\text{ 2 area}}[/tex]triangle 2 area * 10 = 65 in² * 20
triangle 2 area = (65 in² * 20 ) / 10
= 130 in²
The answer is:
The area of the big triangle is 130 in² .
Angles of Polygons The figure below is a pentagon whose interior angles have the same measure.What is the sum of the measures of these 5 angles?
Given the number of sides of a pentagon:
Number of sides = 5
Let's find the sum of the measures of the 5 equal angles.
To find the sum of the measures of interior angles of a polygon, apply the formula:
[tex]S=(n-2)*180[/tex]Where:
n is the number of sides = 5
Thus, we have:
[tex]\begin{gathered} S=(5-2)*180 \\ \\ S=(3)*180 \\ \\ S=540^o \end{gathered}[/tex]Therefore, the sum of the interior angles of the pentagon is 540 degrees.
ANSWER:
540°
Writing about Finding a Percen Explain how to find 27% of 16 using multiplication by a decimal. Then explain how to use estimation to check your answer.
To find 27% of 16 using multiplication by a decimal, we can proceed as follows:
First, convert the number 27 in decimal:
[tex]16\cdot\frac{27}{100}=16\cdot0.27=4.32[/tex]A way to estimate the possible value, we can multiply the number 16 by the nearest tenth, that is, 0.3. We know that the possible value is a little greater than the actual value.
We can do this in the following way:
[tex]16\cdot\frac{30}{100}=\frac{48}{100}=4.8[/tex]Then, after the estimation, we can say that the value must be less than 4.8. Multiplying by 3 or 30 is easier than by 27. This is a way to check the answer.
We can also say that if we multiply 16 by 3 is 48 (equivalently to 4.8, after doing the correct operations), and this is a quick value to know, that, approximately 4.32 is 27% of 16.
What are the possible values for the missing term of the geometric sequence? .004, _____, .4.04.04, -.04.0004.0004, -.0004
By definition, in a Geometric sequence the terms are found by multiplying the previous one by a constant. This constant is called "Common ratio".
In this case, you know these values of the set:
[tex]\begin{gathered} .004 \\ .4 \end{gathered}[/tex]Notice that you can set up this set with the value given in the first option:
[tex].004,.04,.4[/tex]Now you can check it there is a Common ratio:
[tex]\begin{gathered} \frac{0.04}{0.004}=10 \\ \\ \frac{.4}{0.04}=10 \end{gathered}[/tex]The Common ratio is:
[tex]r=10[/tex]Therefore, it is a Geometric sequence.
Apply the same procedure with each option given in the exercise:
- Using
[tex].004,.04,-.04,.4[/tex]You can notice that it is not a Geometric sequence, because:
[tex]\begin{gathered} \frac{-.04}{.04}=-1 \\ \\ \frac{.4}{-.04}=-10 \end{gathered}[/tex]- Using
[tex].004,.0004,.4[/tex][tex]\begin{gathered} \frac{.0004}{.004}=0.1 \\ \\ \frac{4}{.0004}=1,000 \end{gathered}[/tex]Since there is no Common ratio, if you use the value given in the third option, you don't get a Geometric sequence.
- Using this set with the values given in the last option:
[tex].004,.0004,-.0004,.4[/tex]You get:
[tex]\begin{gathered} \frac{.0004}{.004}=0.1 \\ \\ \frac{-.0004}{.0004}=-1 \end{gathered}[/tex]It is not a Geometric sequence.
The answer is: First option.
which is the solution of 3(t + 1) = 6 - 13.5?A <-5.5B t2-5.5Ci< 5.5D (>55
Let's begin by identifying key information given to us:
[tex]\begin{gathered} 3\mleft(t+1\mright)\le6t-13.5 \\ 3t+3\le6t-13.5 \\ \text{Put like terms together, we have:} \\ 3+13.5\le6t-3t \\ 16.5\le3t \\ \frac{16.5}{3}\le\frac{3t}{3} \\ 5.5\le t\Rightarrow t\ge5.5 \\ \therefore t\ge5.5 \end{gathered}[/tex]Therefore, D is the correct answer
20. Two teachers measured the shoe size of each of their students. The datawere used to create the box plots shown.Mrs. Norris's Class567891011121314Shoe SizeMrs. Ganger's Class5 6+87111213149 10Shoe SizeBased on the data, which statement about the results must be true?The average shoe size is the same for both classes.The shoe sizes 6 and 13 are outliers for both classes.© Mrs. Norris's class and Mrs. Ganger's class have the sameinterquartile range.© The median shoe size for Mrs. Norris's class is greater than forMrs. Ganger's class.
The correct answer is the last sentence.
"The median shoe size for Mrs. Norris's class is greater than for
Mrs. Ganger's class".
I'm needing help with graphing equation
what is the equation?
a) y = 2x
x y
1 2(1) = 2
2 2(2) = 4
3 2(3) = 6
4 2(4) = 8
5 2(5) = 10
b) y = x - 2
x y
2 2 - 2 = 0
3 3 - 2 = 1
4 4 - 2 = 2
5 5 - 2 = 3
6 6 - 2 = 4
a) line a
line b
c)
y = 3x + 2
x y
1 3(1) + 2 = 5
2 3(2) +2 = 8
3 3(3) + 2 = 11
4 3(4) + 2 = 14
5 3(5) + 2 = 17
line d
y = 5x - 3
x y
0 5(0) - 3 = -3
2 5(2) - 3 = 7
4 5(4) - 3 = 17
6 5(6) - 3 = 27
Determine if the triangles are similar, if similar state how
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Triangle YXZ
Triangle AXB
Similar Triangles = ?
Step 02:
Similar Triangles
AB || YZ
The Side-Splitter Theorem:
AB || YZ ===> XY/ YA = XZ / ZB
The answer is:
The triangles are similar, by the Side-Splitter Theorem.
Question 8 According to a textbook, this is a challenging question; according to me, it is the easiestquestions, among the easy questions!Suppose that the equations ax + by = c, where a, b, and c are real numbers, describes a directvariation. What do you know about the value of c?That c is
The Solution:
Given the equation below:
[tex]ax+by=c_{}[/tex]We are asked to say what we know about the value of c.
From the above equation, it is clear that:
c is a variable that depends on the values of the variables x and y.(where a and b are possibly constants.
Larry Mitchell invested part of his $17000 advance at 2% annual simple interest and the rest at 5% annual simple interest. If his total yearly interest from both accounts was $610, find the amount invested at each rate
The simple interest is given by:
[tex]SI=Prt[/tex]where P is the principal (the amount we invest in the account), r is the interest rate and t is the time of investment.
Let P be the interest Larry made in the 2% account, the simple interest in this case is given by:
[tex]0.02P[/tex]Now for the second account we would have an envestment of (17000-P), then the simple interest have to be:
[tex]0.05(17000-P)[/tex]and we know that both investments have to be equal to 610, then we have:
[tex]\begin{gathered} 0.02P+0.05(17000-P)=610 \\ 0.02P+850-0.05P=610 \\ -0.03P=610-850 \\ -0.03P=-240 \\ P=\frac{-240}{-0.03} \\ P=8000 \end{gathered}[/tex]Therefore Larry invested $8000 in the 2% account and $9000 in the 5% account.
x=-3
f(x)= -2
f’(x)=2
g(x)=3
g’(x)=-1
h(x) = g(x)/2f(x)
Find h'(-3)
Answer: [tex]-1[/tex]
Step-by-step explanation:
Using the quotient rule,
[tex]h'(x)=\frac{2f(x)g'(x)-2g(x)f'(x)}{(2f(x))^2}\\\\h'(3)=\frac{2f(3)g'(3)-2g(3)f'(3)}{(2f(3))^2}\\\\=\frac{2(-2)(-1)-2(3)(2)}{2(-2)^2}\\\\=-1[/tex]
FIVE STAR®
The cost associated with a school dance is $300 for a venue rental and $24 for each couple
that attends. This can be represented by the expression 300 + 24x.
a. Define all the variables and terms is this scenario. That means tell us what x, 24x, and
300 represent
Answer:
300 -- venue cost24 -- cost for each couplex -- the number of couples24x the cost associated with all couple300+24x -- the total cost for the danceStep-by-step explanation:
Given the scenario that cost is $300 for the venue and $24 for each couple attending a dance at that venue, you want to know the meaning of the variables and terms in 300 +24x.
ComparisonYou can compare the terms, coefficients, and variables in the given expression with the parts of the problem statement.
300 is a constant term that corresponds to "$300 for a venue rental'24 is a coefficient that corresponds to "$24 for each couple"x is a variable representing the number of "couple that attends"24x is a term representing the cost associated with "$24 for each couple that attends"That is, the cost associated with the number of people attending is $24 times the number of couples: 24x. The expression 300+24x is the total of the fixed venue cost and the per-couple costs
I really need help with number 9 find the value of x that makes abcd a parallelogram.
Given:
The adjacent angles of a parallelogram are 78 and x+10.
To find:
The value of x.
Explanation:
We know that,
The sum of the adjacent angles in a parallelogram is supplementary.
So, we can write,
[tex]\begin{gathered} 78+x+10=180 \\ x+88=180 \\ x=180-88 \\ x=92 \end{gathered}[/tex]Thus, the value of x is 92.
Final answer:
The value of x is 92.
Find an angle with θ with 0∘ < θ < 360∘ that has the same :
Sine as 220∘ : θ = _______ degrees
Cosine as 220∘ : θ = _______ degrees
The complete trigonometry ratios are sin(220) = -sin(40) and cos(220) = cos(140) and the angles are 40 and 220 degrees
How to determine the measure of the angles?Angle 1
The trigonometry ratio of the angle is given as
sin(220)
Expand the above expression
sin(220) = sin(180 + 40)
Apply the sine rule
sin(220) = sin(180)cos(40) + cos(180)sin(40)
Evaluate the ratios
sin(220) = 0 x cos(40) - sin(40)
So, we have
sin(220) = - sin(40)
So, the measure of the angle is 40 degrees
Angle 2
The trigonometry ratio of the angle is given as
cos(220)
Expand the above expression
cos(220) = cos(360 - 140)
Apply the cosine rule
cos(220) = cos(360)cos(140) + sin(140)sin(360)
Evaluate the ratios
cos(220) = 1 x cos(140) + sin(140) x 0
So, we have
cos(220) = cos(140)
So, the measure of the angle is 140 degrees
Read more about trigonometry ratios at
https://brainly.com/question/24349828
#SPJ1
A helicopter pilot sights a landmark an an angle of depression of 34°. The altitudeof the helicopter is 1,748 feet. To the nearest foot, what is the horizontal distancefrom the helicopter to the landmark?
For the question, we will be making a sketch showing the features in the question.
From the sketch and the question, the angle of depression = 34 degrees
The helicopter height above the ground (altitude) = 1,748 ft
L represents the landmark
x = horizontal distance from the helicopter to the landmark
To solve the question, we need to bring out the right triangle from the sketch
Angle e = 34 degrees (alternate to the angle of depression given)
To get x, we make use of the trigonometrical ratio of tan
[tex]\begin{gathered} \tan \text{ }\theta=\frac{opposite}{adjacent} \\ \text{From the right triangle, the opposite = 1748} \\ \text{The adjacent = x} \\ \theta=34^0 \\ \tan \text{ 34 =}\frac{\text{1748}}{x} \\ \text{Making x the subject of the formula, we have} \\ x=\frac{1748}{\tan 34} \\ x=\frac{1748}{0.6745} \\ x=2591.55 \end{gathered}[/tex]Therefore, the horizontal distance from the helicopter to the landmark to the nearest foot is 2592 feet.
I need help with #1 of this problem. It has writings on it because I just looked up the answer because I’m confused but I want to know the answer and how to do it with work provided please
In the figure below
1) Using the theorem of similar triangles (ΔBXY and ΔBAC),
[tex]\frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC}[/tex]Where
[tex]\begin{gathered} BX=4 \\ BA=5 \\ BY=6 \\ BC\text{ = x} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \frac{4}{5}=\frac{6}{x} \\ \text{cross}-\text{multiply} \\ 4\times x=6\times5 \\ 4x=30 \\ \text{divide both sides by the coefficient of x, which is 4} \\ \text{thus,} \\ \frac{4x}{4}=\frac{30}{4} \\ x=7.5 \end{gathered}[/tex]thus, BC = 7.5
2) BX = 9, BA = 15, BY = 15, YC = y
In the above diagram,
[tex]\begin{gathered} BC=BY+YC \\ \Rightarrow BC=15\text{ + y} \end{gathered}[/tex]Thus, from the theorem of similar triangles,
[tex]\begin{gathered} \frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC} \\ \frac{9}{15}=\frac{15}{15+y} \end{gathered}[/tex]solving for y, we have
[tex]\begin{gathered} \frac{9}{15}=\frac{15}{15+y} \\ \text{cross}-\text{multiply} \\ 9(15+y)=15(15) \\ \text{open brackets} \\ 135+9y=225 \\ \text{collect like terms} \\ 9y\text{ = 225}-135 \\ 9y=90 \\ \text{divide both sides by the coefficient of y, which is 9} \\ \text{thus,} \\ \frac{9y}{9}=\frac{90}{9} \\ \Rightarrow y=10 \end{gathered}[/tex]thus, YC = 10.
QUESTION 6Emily has enrolled in a first year math class. The course has 5 assignments each worth 2%, 3 tests worth 20% and 2 tests worth 15%. Emily thus far has completed 3 assignments scoring: 72%, 84%, and 58%. In addition to the assignments, Emily has completed 2 tests: Test 1 (worth 20%) she scored 85% and Test 2 she scored 68% (worth 15%). What is Emily's current grade? Keep the answer in percent and round to the tenth if necessary. Do not input the percent (%) into the answer.
ANSWER:
76.8
STEP-BY-STEP EXPLANATION:
Given:
3 Assignments (2%)
1. 72%
2. 84%
3. 58%
1 Test (20%)
85%
1 Test (15%)
68%
We can calculate Emily's current grade using the weighted average principle, just like this:
[tex]p=\frac{\sum ^{}_{}x_i\cdot w_i}{\sum ^{}_{}w_i}[/tex]In this case, the value of x are the scores and w are the percentages associated with that value, we replace:
[tex]\begin{gathered} g=g=\frac{72\cdot2\%+84\cdot2\%+58\cdot2\%+85\cdot20\%+68\cdot15\%}{2\%+2\%+2\%+20\%+15\%} \\ g=\frac{72\cdot0.02+84\cdot0.02+58\cdot0.02+85\cdot0.2+68\cdot0.15}{0.02+0.02+0.02+0.2+0.15} \\ g=\frac{31.48}{0.41} \\ g=76.78 \\ g\cong76.8\% \end{gathered}[/tex]Therefore, Emily's current grade is 76.8%.
What is the measure of ∠N, if ∠M and ∠N are angles in a linear pair and the m∠M is 30°? *.
Given:
[tex]\angle M=30\degree[/tex]And angle M and N are angles in a linear pair.
Required:
To find the angle N.
Explanation:
The sum of angles of a linear pair is always equal to 180°.
Therefore,
[tex]\begin{gathered} \angle M+\angle N=180\degree \\ \\ 30\degree+\angle N=180\degree \\ \\ \angle N=180\degree-30\degree \\ \\ \angle N=150\degree \end{gathered}[/tex]Final Answer:
[tex]\angle N=150\degree[/tex]Use the standard algorithm to solve the equation 36 x 25 =
Answer: 900
Step-by-step explanation:
Column method
Claim: The mean pulse rate (in beats per minute) of adult males is equal to bpm. For a random sample of adult males, the mean pulse rate is bpm and the standard deviation is bpm. Find the value of the test statistic.
For solving this question, you should apply the equation:
The question gives
Next step - replace the values in the equation
[tex]z_T=\frac{70.4-69}{\frac{10.8}{\sqrt[]{129}}}=\frac{1.4}{\frac{10.8}{\sqrt{129}}}=1.47[/tex]3-4 Ch 8 L 5-7 Test (modified) Is the given value a solution of the inequality? 2 + m > 10 m = 7
2 + m > 10
substituting with m = 7, we get:
2 + 7 > 10
9 > 10
which is false, because 9 is less than 10
What fraction of $36,000 is $27,000?
We need to keep in mind that
36000 is 1
In order to know the fraction we need to divide 27000 between 36000, and then simplify the fraction
[tex]\frac{27000}{36000}=\frac{27}{36}=\frac{3}{4}[/tex]the fraction of 36000 that is 27000 is 3/4
How many square feet of outdoor carpet willwe need for this hele??3 ft2 ft2 ft
total square feet:
[tex]4\times12=48\text{ ft}[/tex]square feet 1:
-1010The graph of the equation y - 272. 2 is shown. Which equation will shift the graph up 3 units?A)ya 2x²y=2x-1y=2x²-3D)y = 2(x+3)²
f(x) + 3, translates f(x) 3 units up
In this case, the function is y = 2x² - 2.
Applying the above rule, we get:
y = 2x² - 2 + 3
y = 2x² + 1
Given the parametric equations x = 7cos θ and y = 5sin θ, which of the following represents the curve and its orientation?
We have the following parameters
[tex]\begin{gathered} x=7cos\theta \\ y=5sin\theta \end{gathered}[/tex]the general equation of a circle with center (0,0) is the following,
[tex]x^2+y^2=r^2[/tex]Let's use the following tigonometric identity,
[tex]sin^2\theta+cos^2\theta=1[/tex]solving for cos and sin in the equations we are given,
[tex]cos\theta=\frac{x}{7},sin\theta=\frac{y}{5}[/tex]replace,
[tex](\frac{y}{5})^2+(\frac{x}{7})^2=1[/tex]Since we have two different numbers in the denominator, this is not a circle equation but an elipse, of the form,
[tex]\frac{y^2}{a^2}+\frac{x^2}{b^2}=1[/tex]where,
a is the vertex and,
b is the covertex
thus, in the x axis, the vertex is 7 and the y-axis the covertex is 5
Now, let's determine the direction by replacing
when Θ = 0 , then x = 7*cos0 = 7*1 = 7 , and y = 5*sin0 = 5*0 = 0
when Θ = 90° or π/2 , then x = 7*cos90° = 7*0 = 0 , and y = 5sin90° = 5*1 = 5
If we draw this, we can see that the direction is counterclockwise as in the bottom right image.
Daisy is buying a video game in the shop. The price before tax is $21, and after sales tax is $24.74. What is the sales tax plied to the video game? Round to the nearest hundredth
Recall that:
[tex]\text{salesprice}=\text{originalprice+taxes.}[/tex]Therefore Daisy pays:
[tex]24.74-21=3.74\text{ dollars}[/tex]in taxes for the videogame.
Now, recall that to determine the percentage that a represents from b we use the following expression:
[tex]\frac{a}{b}\cdot100.[/tex]Therefore, the sales tax applied to the videogame is:
[tex]\frac{3.74\text{dollars}}{21\text{dollars}}\cdot100\approx17.81[/tex]percent.
Answer: The tax applied to the videogame is 17.81%, in this case, the sales tax is 3.74 dollars.