Given the Quadratic Equation:
[tex]x^2-9x-36=0[/tex]You need to remember that the Zero Product Property states that if:
[tex]ab=0[/tex]Then:
[tex]a=0\text{ }or\text{ }b=0[/tex]In this case, you can factor the given equation by finding two numbers whose sum is -9 and whose product is -36. These numbers are 3 and -12. Then:
[tex](x+3)(x-12)=0[/tex]Based on the Zero Product Property, you know that:
[tex](x+3)=0\text{ }or\text{ }(x-12)=0[/tex]Then, by solving each part by "x", you get:
[tex]x=-3\text{ }or\text{ }x=12[/tex]Hence, the answer is:
[tex]x=-3\text{ }or\text{ }x=12[/tex]A triangle with side lengths 8, 15, and 17 is a right triangle by theconverse of thePythagorean Theorem. What are the measures of the other 2 angles?Round your answers to the nearest whole number.HINT: Draw a diagram of this problem and label your triangle.The méasure of the smaller acute angle is ____degreesand the larger acute angle measures_______degrees.
We are given a right-angle triangle with side lengths 8, 15, and 17.
Since it is a right triangle, one angle must be 90°
Let us find the other two angles of this right triangle.
With respect to angle x, the opposite side is 15 and the hypotenuse side is 17.
Recall from the trigonometric ratios,
[tex]\begin{gathered} \sin (x)=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin (x)=\frac{15}{17} \\ x=\sin ^{-1}(\frac{15}{17}) \\ x=61.9\degree \end{gathered}[/tex]So, the second angle is 61.9°
Recall that the sum of angles inside a triangle must be equal to 180°
So, the third angle can be found as
[tex]\begin{gathered} y+61.9\degree+90\degree=180\degree \\ y=180\degree-90\degree-61.9\degree \\ y=28.1\degree \end{gathered}[/tex]So, the third angle is 28.1°
The measure of the smaller acute angle is 28.1 degrees and the larger acute angle measures 61.9 degrees.
The missing side length in the right triangle is __ cm.
364
1) Assuming this is a right triangle, the side whose length is 365 is the hypotenuse, so we can write out the Pythagorean Theorem:
365² = 27² +c²
133225 =729+ c²
133225 -729 = c²
132496= c² Take the square root on both sides
√132496 = √c²
c = 364
2) Hence, the missing leg is 364 cm
What is the probability that Erika will get to move ahead on this spin.
total outcomes=8
move ahead outcome=4
probabilty of move ahead =4/8=1/2
Thus the answer is 1/2.
Two birds spot a cat trying to jump up to their cage Find the angle of depression of the cat.
Step 1
Draw the triangle for clarity
From the diagram above it is clear, the angle of depression is equal to the angle of elevation since both angles are alternate interior angles. Therefore, we can go ahead to find the angle of elevation which is equal to the angle of depression.
Step 2
Find the angle of depression using SohCahToa
To find this angle we will use the ratio Cah written as
[tex]\begin{gathered} \cos x=\frac{adjacent}{\text{hypotenuse}} \\ \text{adjacent}=4ft \\ \text{hypotenuse}=5ft \end{gathered}[/tex][tex]\begin{gathered} \cos x=\frac{4}{5} \\ x=\cos ^{-1}(\frac{4}{5}) \\ x=36.86989765^{\circ}_{} \\ x\approx36.9^{\circ}\text{ to 1 decimal places} \end{gathered}[/tex]Hence the angle of depression of the cat, x to 1 decimal place = 36.9°
A real estate agent works on a 11 % commission. What is her commission on a house that she sold for $597,000?Follow the problem-solving process and round your answer to the nearest cent, if necessary.
Given:
11% commission.
House sold is $597, 000
To find the commission on a house she sold for $597 000, simply find 11 % of that amount.
That is;
Her commision = 11% of $597,000
[tex]=\frac{11}{100}\times597000[/tex][tex]=\text{ 6567000/100}[/tex][tex]=\text{ \$65670}[/tex]Hence, her commision is $65670
The legs of a right triangle measure 29 centimeters and 95 centimeters. How long is the hypotenuse in centimeters?
In this question, the two legs of a right angle triangle are:
29 centimeters and 95 centimetres
To find the hypotenuse, let's use Pythagoras Theorem.
[tex]c^2=a^2+b^2[/tex]where ,
a = 29 centimeters
b = 95 centimeters
c = hypotenuse
Therefore,
[tex]c^2=29^2+95^2[/tex][tex]c^2\text{ = 841 + 9025}[/tex][tex]c^2\text{ = 9866}[/tex]Now take the square root of both sides
[tex]\sqrt{c^2\text{ = }}\sqrt{9866}[/tex][tex]c\text{ = 99.327}[/tex]The hypotenus in centimeter is 99.3 centimeters
The Homecoming committee wants to raise between $1500 and $2000 at the dance.They have already saved $800 to put towards the dance. If tickets are $20 each, howmany tickets must they sell? Variable Represents:Inequality:Solve:Sentence:
Answer:
35≤t≤60
Explanation:
Let the variable t represents the number of tickets they must sell.
Cost of a ticket =$20
• Cost of t tickets =$20t
Since they have already saved $800
Total balance = 800+20t
The committee wants to raise between $1500 and $2000 at the dance.
Therefore, the inequality representing this situation is:
[tex]1500\leqslant800+20t\leqslant2000[/tex]We solve for t.
[tex]\begin{gathered} 1500\leqslant800+20t\leqslant2000\text{ (Subtract 800 from all sides)} \\ 1500-800\leqslant800-800+20t\leqslant2000-800 \\ 700\leqslant20t\leqslant1200\text{ (Divide all through by 20)} \\ \frac{700}{20}\leqslant\frac{20t}{20}\leqslant\frac{1200}{20} \\ 35\leqslant t\leqslant60 \end{gathered}[/tex]The homecoming committee must sell between 35 and 60 tickets to meet their goal.
If the side ratio is 4:17, the the area ratio is
The Solution:
Given the side ratio below:
[tex]4\colon17[/tex]We are asked to find the area ratio of the figures being compared.
While the ratio of sides is linear, the ratio of area is square.
This means that if:
[tex]\begin{gathered} \text{ side ratio =4:17} \\ \text{Then it follows that} \\ \text{area ratio will be} \\ \text{ 4}^2\colon17^2=16\colon289 \end{gathered}[/tex]Therefore, the correct answer is [ 16:289 ]
hi thank you for helping me . is this just multiplication?
ANSWER:
25.84
STEP-BY-STEP EXPLANATION:
To multiply two decimal numbers:
1. They are multiplied as if they were whole numbers.
2. The final result is a decimal number whose number of decimal places is equal to the sum of the number of decimal places of the two factors.
Therefore:
Which of the following is NOT a level of measurement?Choose the correct answer below.A) OrdinalB) NominalC) RatioD)Quantitative
Given:
A) Ordinal
B) Nominal
C) Ratio
D)Quantitative
Required:
We want to find that Which of the given is NOT a level of measuremen
Explanation:
Levels of Measurement Nominal, Ordinal, Interval and Ratio
but the Quantitative is not the Levels of Measurement because it is
M O GEOMETRY Identifying parallelograms, rectangles, and squares Answer the questions about the figures below. 3 m Figure A Explanation 3 m 3 m (a) Which figures are squares? Mark all that apply. Figure A (b) Which figures are parallelograms? Mark all that apply. O Figure A O Figure B (c) Which figures are rectangles? Mark all that apply. O Figure A 3 m O Figure B O Figure C Figure B Check O Figure C O Figure C Figure B 2 m 5 m 4 m O None of the figures O None of the figures O None of the figures 3 m L X Figure C 5 m 5 m ☐ L ? 3 m 0/5 O2022 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center Nikid Ac
Given the dimensions of each figure:
• Figure A:
Length of each side = 3m
All sides have equal lengths.
• Figure B:
Length of top base = 2 m
Length of bottom base = 5m
Length of each leg = 4m
• Figure C.
Length = 5 m
Width = 3m
Since the length of all sides in figure A are equal and they meet at right angles, we can say figure A is a square.
Also, figure A has 2 pairs of parallel sides.
Since it has 2 pairs of parallel sides, we can say it is also a parallelogram.
Figure B has two parallel bases, while the opposite legs are equal.
Figure B has just one pair of parallel side.
Thus, we can figure B is a trapezoid.
Figure C has two pairs of parallel sides and the opposite sides have equal lengths.
Thus, we can say Figure B is rectangle and also a parallelogram.
Hence, we have the following:
• Squares ==> Figure A
,• Parallelogram ==> Figure A and Figure C
,• Rectangle ==> Figure C.
• ANSWER:
(a).
(c).
solve the following equation, write the answer in reduced fraction form, if necessary. (x+5)(x-5)=0Separate multiple entries with commas.
Section 1.5: Mortgages and Credit Cards8. A car costs $10,500, and you're offered a loan that requires $800 down and a monthly payment of $187.53 for 60 months, how much will you pay in interest? Round your answer to the nearest dollar.$
A monthly payment of $187.53 for 60 months will give us:
[tex]187.53\times60=\text{ \$11,251.8}[/tex]The total money paid is:
[tex]\begin{gathered} \text{the down payment of \$800 + \$11,251}.8 \\ \Rightarrow800+11,251.8=12051.8 \end{gathered}[/tex]Hence, the interest paid is:
[tex]\begin{gathered} 12,051.8-10,500 \\ \Rightarrow\text{ \$}1551.8 \end{gathered}[/tex]In AFGH, the measure of ZH=90°, GF = 89, HG = 80, and FH = 39. What ratiorepresents the cotangent of ZF?
cotangent ZF = adjacent side / opposite side
adjacent side = 39
opposite side = 80
cotangent ZF = 39/80
The data for the control group has a a. first common differenceb. second common difference c. common ratioTherefore the data is being generated by a a. linear functionb. quadratic function c. exponential functionThe data for the original formula has aa. first common difference b. second common differencec. common ratioTherefore the data is being generated by a a. linear functionb. quadratic functionc. exponential function The data for the improved formula has a a. first common difference b. second common difference c. common ratio Therefore the data is being generated by a a. linear functionb. quadratic functionc. exponential function
Answer:
The data for the control group has a first common difference, therefore the data is being generated by a linear function
The data for the original group has a second common difference, therefore the data is being generated by a quadratic function
The data for the Improved group has a common ratio, therefore the data is being generated by an exponential function
Explanation:
Given the table in the attached image.
The data for the control group has a common difference, that is the difference between consecutive values are the same.
[tex]d=13-6=20-13=27-20=34-27=41-34=7[/tex]Since the values have a common difference then it is a linear function.
The original formula has a second common difference, therefore the data is being generated by a quadratic function.
The improved formula has a common ratio;
[tex]r=\frac{18}{9}=\frac{36}{18}=\frac{72}{36}=\frac{144}{72}=\frac{288}{144}=2[/tex]Therefore, the data is being generated by an exponential function.
Find the slope of the line that passes through the points (15,-2) and (5,-4).Write answer as an integer or a reduced fraction
1) To find the slope of the line that passes through those points, we'll need to use the Slope Formula
[tex]\begin{gathered} m=\frac{y_2-y_1_{}}{x_2-x_1} \\ m=\frac{-4-(-2)}{5-15}=\frac{-4+2}{-10}=\frac{-2}{-10}=\frac{-1}{-5}=\frac{1}{5} \end{gathered}[/tex]Note that the slope is the measure of how steep is the line between those points.
2) That is the answer.
5. Elena wanted to find the slope and y-intercept of the graph of 25x - 20y = 100.She decided to put the equation in slope-intercept form first. Here is her work-25x – 20y = 10020y = 100 – 25x5y = 5 --X-5. Describe Elena's mistake in her work above, and what the correct slopeand y-intercept of the line are.What are the x- and y-intercepts of the equation 4y + 9x = 18?
Given the equation:
25x - 20y = 100
Let' write the equation in slope-intercept form and find the mistaeke in Elena's worl.
Apply the slope intercept form of a linear equation:
y = mx + b
Rewrite the equation for y:
25x - 20y = 100
• Subtract 25x from both sides:
25x - 25x - 20y = 100 - 25x
-20y = 100 - 25x
• Divide all terms by -20:
[tex]undefined[/tex]a pizza song head offer 6 kinds of meat toppings and 6 vegetable topping and how many different ways could you select a meat topping and in vegetable topping
A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with sigma equals 19.0 milligrams. Construct a 95% confidence interval for the true mean cholesterol content u of all such eggs.
ANSWER
[tex]223.88,232.11[/tex]EXPLANATION
Given;
[tex]\begin{gathered} n=82 \\ \bar{x}=228 \\ \sigma=19.0 \\ \end{gathered}[/tex]At 95% confidence level;
[tex]\begin{gathered} \propto=1-95\% \\ =1-0.95 \\ =0.05 \\ \frac{\propto}{2}=0.025 \\ Z_{\frac{\operatorname{\propto}}{2}}=Z_{0.025}=1.96 \\ \end{gathered}[/tex]At 95% confidence interval for true mean;
[tex]\begin{gathered} \bar{x}\pm Z_{\frac{\operatorname{\propto}}{2}}\frac{\sigma}{\sqrt{n}} \\ =228\operatorname{\pm}1.96\times\frac{19}{\sqrt{82}} \\ =228+1.96\times\frac{19}{\sqrt{82}}<228-1.96\times\frac{19}{\sqrt{82}} \\ =228-4.1124<228+4.1124 \\ =223.88<\mu<232.11 \end{gathered}[/tex]Therefore, 95% confidence interval for the true mean cholesterol content
(223.88,232.11)
Frank has a vintage comic book worth $454. According to a dealer, the value of this particular comic book will increase by 15% each year. How much will the comic book be worth in 2 years?If necessary, round your answer to the nearest cent.
Given:
Current worth = $454
Rate of increase = 15% = 0.15
Time = t
To find how much the book will be worth in 2 years, apply the exponential growth formula:
[tex]y=a(1+r)^t[/tex]Where:
a is the current worth = 454
r is the rate of increase = 0.15
t is the time = 2 years
Hence, we have:
[tex]\begin{gathered} y=454(1+0.15)^2 \\ \\ y=454(1.15)^2 \\ \\ y=454(1.3225) \\ \\ y=600.42 \end{gathered}[/tex]Therefore, the worth of the comic book in 2 years is $600.42
ANSWER:
$600.422 ye
What is the volume of this sphere?Use3.14 and round your answer to the nearest hundredth.4 mcubic metersHELPP!!!
Answer:
Explanation:
The formula for the area of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]Where r is the radius of the circle.
In this case, the diameter of the circle is 6in, then;
[tex]r=\frac{6in}{2}=3in[/tex]The volume is:
[tex]undefined[/tex]1x-5x? please help me !
Use the unit circle to identify the reference angle for 155°.
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define Unit circle
[tex]undefined[/tex]J(7, -2), K(-4, 9), L(-3,-1)
If cosθ=3√2cosθ=32 then which of the following could be true?tan=−3√tangent is equal to negative square root of 3cscθ=12cosecant theta is equal to 1 halfsecθ=−2secant theta is equal to negative 2sinθ=2√2sine theta is equal to the fraction with numerator square root of 2 and denominator 2
Given that
[tex]\cos\theta=\frac{\sqrt{3}}{2}[/tex]we can determinate the sine of this angle using the following identity
[tex]\sin^2\theta+\cos^2\theta=1[/tex]If we substitute the value of the cosine on this identity, we're going to have:
[tex]\begin{gathered} \sin^2\theta+(\frac{\sqrt{3}}{2})^2=1 \\ \sin^2\theta+\frac{3}{4}=1 \\ \sin^2\theta=\frac{1}{4} \\ \sin\theta=\pm\frac{1}{2} \end{gathered}[/tex]The definitions of secant, tangent, and cosecant in terms of the sine and cosine are given by:
[tex]\begin{gathered} \tan\theta=\frac{\sin\theta}{\cos\theta} \\ \sec\theta=\frac{1}{\cos\theta} \\ \csc\theta=\frac{1}{\sin\theta} \end{gathered}[/tex]Using the known values for the sine and cosine functions on those definitions, we have:
[tex]\begin{gathered} \tan\theta=\frac{\pm\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\pm\frac{1}{\sqrt{3}}=\pm\frac{\sqrt{3}}{3}\ne-\sqrt{3} \\ \\ \csc\theta=\frac{1}{\pm\frac{1}{2}}=\pm2\ne\frac{1}{2} \\ \\ \sec\theta=\frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}}=\frac{2\sqrt{3}}{3}\ne-2 \\ \\ \sin\theta=\pm\frac{1}{2}\ne\frac{\sqrt{2}}{2} \end{gathered}[/tex]All options are false.
im completely lost on my review it says find the missing angle from these 2 congruent triangles.
We will reason to find the values of angles 1 through 6. To do so, we will use a key fact of triangles which is:
the sum of the angles of a triangle is 180°.
So, we will start by finding the value of angle 1. Note that angle 1 is in the triangle XYZ, whose other angles are 58° and 65°. Then, we have the following equation
[tex]\text{Angle 1 + 58\degree+65\degree=180\degree}[/tex]Since 58+65 = 123 then we have
[tex]\text{Angle 1 + 123 =180}[/tex]By subtracting 123 on both sides, we get that
[tex]\text{Angle 1 =180-123 = 57\degree}[/tex]So angle 1 measures 57°.
We can see that angles 1 and 2 are supplementary. That is, their measures add up to 180°. So, we have the following equation
[tex]\text{Angle 1 + Angle 2 =180}[/tex]Since angle 1 = 77° we have that
[tex]77\text{ + Angle 2 = 180}[/tex]which implies that angle 2 measures 123°. Using the same principle we can find the value of angle 5, since we have
[tex]\text{Angle 2 + Angle 5 = 180}[/tex]since angle 2 measures 123, we have that
[tex]123+\text{ Angle 5 = 180}[/tex]which implies that angle 5 measures 57°. Now, we see that angle 6 is in triangle VXW, so we can find the value of angle 6 as follows
[tex]\text{Angle 6 + Angle 5 + 67 = 180}[/tex]Then, since angle 5 measures 57° we have
[tex]\text{Angle 6 + 57\degree+67\degree=180\degree}[/tex]Since 57+67=124. Then , we have
[tex]\text{Angle 6 + 124 = 180 }[/tex]Subtracting 124 on both sides, we get
[tex]\text{Angle 6 = 180-124 = 56}[/tex]Now, we are missing to find the values of angles 3 and 4. To do so, first notice that
[tex]\text{Angle 2 + Angle 3 +Angle 4=180}[/tex]since these are the angles of triangle WXZ. We already know the measure of the angle 2 (123), so we have
[tex]\text{Angle 3 + Angle 4 =}180\text{ -123 = 57}[/tex]Unfortunately, the question doesn't give any more details on the triangles, so there are multiple solutions of values of angles 3 and 4 such that the equation holds
wgat us 5he image of (0,-1) after a translation of left 5 units and down 1 unit
EXPLANATION
Given the point (0,-1), after a translation of left 5 units and down 1 unit the image would be:
Image: (-5,-2)
Solve the equation: √ t − 13 = 4 Answer: t =
Taking the given equation to the power of 2 we get:
[tex](\sqrt{t-13})^2=4^2.[/tex]Simplifying the above result we get:
[tex]t-13=16.[/tex]Adding 13 to the above equation we get:
[tex]\begin{gathered} t-13+13=16+13, \\ t=29. \end{gathered}[/tex]Answer: t=29.
Find the sum of 5 even positive integers
sum of 5 even positive integers
[tex]n+(n+2)+(n+4)+(n+6)+(n+8)[/tex]here, n is the first even number,
let's simplify this,
[tex]\begin{gathered} =n+n+2+n+4+n+6+n+8 \\ =5n+20 \end{gathered}[/tex]Thus the expression to find the sum of 5 consecutive even positive integers is, 5*n + 20 , where n is the 1st even positive integer.
let's use it when n = 2 or to sum 2, 4, 6, 8 and 10
[tex]5*2+20=10+20=30[/tex]which is the same as,
[tex]2+4+6+8+10=30[/tex]write the sum in unit form. 4 fifths + 3 fifths =
We write it as follows:
[tex]\frac{4}{5}+\frac{3}{5}=\frac{7}{5}=1\frac{2}{5}[/tex]It is 1 unit and 2/5.