Answer:
3. √74
Explanation:
By the Pythagorean theorem, the length of the hypotenuse can be calculated as:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Where c is the hypotenuse and a and b are the lengths of the legs.
So, replacing a by 5 and b by 7, we get:
[tex]\begin{gathered} c=\sqrt[]{5^2+7^2} \\ c=\sqrt[]{25+49} \\ c=\sqrt[]{74} \end{gathered}[/tex]Therefore, the answer is 3. √74
Which pairs of figures are congruent? Which pairs are similar?The first question.
Given the two circles shown in the exercise, you need to remember that, by definition, two figures are congruent when they have the same size and they have the same shape.
In this case, you can identify that the circles have the same diameters (remember that a diameter of a circle is the length that passes through the center of the circle and touch two points on the circumference):
[tex]\begin{gathered} d_1=2units \\ d_2=2units \end{gathered}[/tex]Therefore, these circles have the same shape and size.
By definition, two figures are similar when their corresponding angles are congruent and the ratios of the corresponding sides are proportional.
In this case, since the figures are circles, you know that they both measure 360 degrees. Knowing that they also have the same diameter, you can determine that they are similar too.
Hence, the answer is: They congruent and similar.
Hey can someone please help me with this problem? I would appreciate the help tysm!
Answer:
18m2
Step-by-step explanation:
Hello, I need help with this precalculus homework question, please?HW Q8
Solution
Given the logarithmic statement below
[tex]\ln7=x[/tex]To change the statement to an exponential statement, we apply an exponent to both sides
[tex]e^{\ln7}=e^x[/tex]Simplifying the expression above gives
[tex]\begin{gathered} 7=e^x \\ e^x=7 \end{gathered}[/tex]Hence, the exponential statement is
[tex]e^x=7[/tex]Sam gave the mother the child a bottle medication and told her a day . the following conversion laclors : 1 - 30 . 1lb(s) = 15mLHow many tablespoon is one dose?How many mL will the child take in one day?How many fl oz is this?How many days will the bottle and medication last?
Given:
The doctor gave the mother of the sick baby 16 fl oz bottle of liquid medicine.
Dosage instructed to give the baby = 30 ml twice a day
a) How many tablespoon is one dose?
Using standard measurements, 1 tablespoon = 15 ml
Since 1 dose is 30 ml, the dose in tablespoon is:
[tex]\frac{30\text{ ml}}{15\text{ ml}}=\text{ 2 tablespoons}[/tex]1 dose is 2 tablespoons
b) Since, 30 ml is to be given 2 times daily, the ml the child will take a day is:
[tex]30\text{ mL }\ast\text{ 2 = 60 mL}[/tex]The child will take 60 mL a day
c) fl oz means fluid ounce
Also 1 fluid ounce is equivalent to 28.41 ml
Given:
28.41ml = 1 fl oz
60 ml =
[tex]\frac{60}{28.41}=2.11\text{ fl oz}[/tex]Therefore, 60 ml = 2.11 fl oz
d) How many days will the bottle and medication last?
To find the number of days the medication will last, we have:
[tex]\frac{16\text{ fl oz}}{2.11\text{ fl oz}}=\text{ 7.6}[/tex]Therefore, the bottle will last for approximately 8 days.
ANSWER:
a) 2 tbs
b) 60 ml
c) 2.11 fl oz
d) Approximately 8 days
Amount of $28,000 is borrowed for nine years at 3.25 interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?Round your answer to the nearest dollar$=
Given:
Principal amount = $28,000
Time period = 9 years
Interest rate = 3.25
Required:
Find the total amount at the end of the period.
Explanation:
The amount formula when the interest is compounded annually is given by the formula:
[tex]A=P(1+r)^{nt}[/tex]Where P =principal amount
r = rate of interest
T = time period
n = Number of time
Substitute the given values in the amount formula.
[tex]\begin{gathered} A=28,000(1+0.0325)^9 \\ A=28,000(1.33355) \\ A=37,339.51 \\ A=37,340 \end{gathered}[/tex]Final Answer:
Thus the amount after 9 years is $37,340.
Hayden has read 3/5 of a book she has read 75 pages so far how many pages are in the whole book?
Let there are x number of pages in whole book. So 3/5 of a book is equal to 3/5x.
Determine the value of x.
[tex]\begin{gathered} \frac{3}{5}x=75 \\ x=75\cdot\frac{5}{3} \\ =125 \end{gathered}[/tex]So there are 125 pages in the whole book.
in rectangle QRST , QS = 3x+7 and RT = 5X-3.find the lengths of the diagonals of QRSTeach diagonal has a length of ....... units.
Consider the rectangle drawn below,
Consider the properties of rectangle that the opposite sides are equal, and both the diagonals are also equal in length.
[tex]QS=RT\Rightarrow3x+7=5x-3\Rightarrow5x-3x=7+3\Rightarrow2x=10\Rightarrow x=5[/tex]Thus, the value of 'x' is 5.
Substitute the value to obtain the diagonal QS as,
[tex]QS=3(5)+7=15+7=22[/tex]Similarly solve for the diagonal RT as,
[tex]RT=5(5)-3=25-3=22[/tex]Already we knew that the diagonal will be equal with the length 22 units.
The measurement of three angles of a triangle are (2x)degrees ,(3x)degrees and (x+30) degrees. What is the value of x?
We have that the measurement of three angles of a triangle is:
1. Angle 1: 2x degrees.
2. Angle 2: 3x degrees.
3. Angle 3: (x+30) degrees.
We know that the sum of the internal angles of a triangle is equal to 180.
Therefore, to find the value of x, we can proceed as follows:
[tex]\begin{gathered} m\angle1+m\angle2+m\angle3=180^{\circ} \\ \\ 2x+3x+(x+30)=180^{\circ} \end{gathered}[/tex]Now, we can add the like terms as follows:
[tex]\begin{gathered} 2x+3x+x+30^{\circ}=180^{\circ} \\ \\ 5x+x+30^{\circ}=180^{\circ} \\ \\ 6x+30^^{\circ}=180^{\circ} \end{gathered}[/tex]We can subtract 30 degrees to both sides of the equation, and then we have to divide both sides by 6:
[tex]\begin{gathered} 6x+30^{\circ}-30^{\circ}=180^{\circ}-30^{\circ} \\ \\ 6x=150^^{\circ} \\ \\ \frac{6x}{6}=\frac{150}{6} \\ \\ x=25 \end{gathered}[/tex]Therefore, in summary, the value for x is equal to 25.
Identify p, q, and r if necessary. Then translate each argument to symbals and use a truth table to decide if the argument is valid or invalid.
Let p denote the statement "It snows", and q denote tthe statement "I can go snowboarding"
The we need to draw a table for
(p => q)v(-p => q)
p q -p -q p=>q -p => -q (p => q)v(-p => q)
T T F F T T T
T F F T F T T
F T T F T F T
F F T T T T T
The argument is valid, since the last column has truth all through.
Hello, Im trying to help my 9th grade daughter who is autistic with her test corrections. Its been over 20 years since I last took Algebra 1 and Im a bit rusty. She gets agitated easily and so Im trying to do some of the prep work now so I can help her when she gets home. I appreciate your assistance in advance
The original graph is given below
a. If the starting number of players is 600 instead of 400 then
The y-intercept will be 600
The new graph will be a vertical stretch of the original graph by a scale factor of 600/400
[tex]\frac{600}{400}=1.5[/tex]Therefore,
The y-intercept will be 600. The new graph will be a vertical stretch of the original graph by a scale factor of 1.5
b. If the starting number of players is 800 instead of 400 then
The y-intercept will be 800
The new graph will be a vertical stretch of the original graph by a scale factor of 800/400
[tex]\frac{800}{400}=2[/tex]Therefore,
The y-intercept will be 800. The new graph will be a vertical stretch of the original graph by a scale factor of 2
Option for the first box: 25, 54, 50, 4Options for the second box:0.5, 2, -0.5, 1Options for the third box:0, 1, 0.5, -0.5 Options for the fourth box:4, 25, 29, 54
Answer:
First box: 25
Second box: 1
Third box: -0.5
Fourth box: 29
First, we will find the amplitude of the sine function.
Hi, can you help me to solve this exercise please!
Step 1:
Write the equation
[tex]\sin (\theta\text{) = }\frac{5}{13}[/tex]Step 2:
Write the trigonometric inverse identity
[tex]\csc (\theta)\text{ = }\frac{1}{\sin \theta}[/tex]Step 3:
Substitute in the equation
[tex]\begin{gathered} \csc (\theta)\text{ = }\frac{1}{\frac{5}{13}} \\ \csc (\theta)\text{ = }\frac{13}{5} \end{gathered}[/tex]Final answer
[tex]csc(\theta)\text{ = }\frac{13}{5}[/tex]4. Multiply the two polynomials using the destructive property.5. Are the two products the same when you multiply them horizontally?4. A)
Given:
[tex](4x^2-4x)(x^2-4)[/tex]To multiply the two polynomials using the distributive property, we first follow the rule shown below:
For: (a+b)(c+d)=a(c+d)+b(c+d)=ac+ad+bc+bd
We let:
[tex]\begin{gathered} a=4x^2 \\ b=-4x \\ c=x^2 \\ d=-4 \end{gathered}[/tex]Now, we plug in what we know:
[tex]\begin{gathered} (4x^{2}-4x)(x^{2}-4) \\ =(4x^2)(x^2)+(4x^2)(-4)+(-4x)(x^2)+(-4x)(-4) \\ Simplify\text{ and rearrange} \\ =4x^4-16x^2-4x^3+16x \\ =4x^4-4x^3-16x^2+16x \end{gathered}[/tex]Therefore, the answer is:
[tex]=4x^4-4x^3-16x^2+16x[/tex]step by step on how to solve 3/4 - 1/2 × 7/8
EXPLANATION
Given the following operation:
3/4 - 1/2*7/8
First, let's solve 1/2*7/8:
Multiply fractions: a/b* c/d = (a*c)/(b*d)
[tex]=\frac{1\cdot7}{2\cdot8}[/tex]Multiply the numbers: 1*7 = 7
[tex]=\frac{7}{2\cdot8}[/tex]Multiply the numbers 2*8=16
[tex]=\frac{3}{4}-\frac{7}{16}[/tex]Now, we need the Least Common Multiplier of 4, 16:
The LCM of a, b is the samllest positive number that is divisible by both a and b:
Prime factorization of 4:
4 divides by 2 ---> 4= 2*2
2 is a primer number, therefore no further factorization is possible.
Prime factorization of 16:
Multiply each factor the greatest number of times it occurs in either 4 or 16
= 2*2*2*2
Multiply the numbers: 2*2*2*2 = 16
Adjust fractions based on LCM
For 3/4: multiply the denominator and numerator by 4
[tex]\frac{3}{4}=\frac{3\cdot4}{3\cdot4}=\frac{12}{16}[/tex][tex]=\frac{12}{16}-\frac{7}{16}[/tex]Since the denominators are equal, combine the fractions:
[tex]=\frac{12-7}{16}[/tex]Subtract the numbers: 12-7 = 5
[tex]=\frac{5}{16}[/tex]Which equation shows that the Pythagorean identity is true for 0=3pi/2
Answer:
Given that,
To find the equation which shows Pythagoras identity is true for theta=3 pi/2
The equation is of the form,
[tex]\sin ^2(\frac{3\pi}{2})+\cos ^2(\frac{3\pi}{2})=1[/tex]we have that,
[tex]\frac{3\pi}{2}=\pi+\frac{\pi}{2}[/tex]Using this we get,
[tex]\begin{gathered} \sin \frac{3\pi}{2}=\sin (\pi+\frac{\pi}{2}) \\ =-\sin (\frac{\pi}{2}) \\ \sin \frac{3\pi}{2}=-1----\mleft(1\mright) \end{gathered}[/tex][tex]\cos \frac{3\pi}{2}=\cos (\pi+\frac{\pi}{2})=0-----(2)[/tex]Substitute the values in the given equation we get,
[tex](-1)^2+0^2=1[/tex]Answer is: Option B:
[tex](-1)^2+0^2=1[/tex]7. How many prime factors does the number 124 have?
It a popular math theorem, that any natural number can be factored out into prime numbers. For example the number 24 is factored as 2³*3, so its prime factors are 2 and 3.
In this case, we want to factor 124. We start by noticing that 124 is an even number, therefore, the first prime factor we try is 2. Next, we divide 124 by 2. We get
[tex]\frac{124}{2}=62[/tex]which is again an even number. This means that we can again divide by 2. We do so
[tex]\frac{62}{2}=31[/tex]Note that 31 is a prime number. So we can't continue dividing. Then
[tex]124=2\cdot2\cdot31=2^2\cdot31[/tex]So it has 2 different prime factors
Based only on the information given in the diagram, which congruencetheorems or postulates could be given as reasons why ACDE=A OPQ?Check all that apply.СA. ASAB. HAC. SASD. LLE. HLF. AAS
The postulates of congruence for right triangles are
• Hypotenuse-Leg Theorem.
,• Leg-Leg Theorem.
,• Leg-Acute Angle Theorem.
,• Hypotenuse-Acute Angle Theorem.
In this case, we know that sides CE and OQ are congruent. (hypotenuses are congruent)
Angle C is congruent to angle O.
Angle E is congruent to angle Q.
To demonstrate the congruence between triangles we can use Hypotenuse-Acute Angle Theorem since they are congruent between triangles.
We can also use Hypotenuse-Leg Theorem because we have corresponding legs and hypotenuses congruent.
The hypotenuse-acute angle theorem states that two right triangles are congruent if they have congruent hypotenuse and one corresponding pair of acute angles congruent.
The hypotenuse-leg theorem states that two right triangles are congruent if they have congruent hypotenuse and one corresponding pair of congruent legs.
Therefore, the right choices are B and E.a hotel claims that 95% of its customers are very satisfied with its service. there is a sample size of seven customers. A. what is the probability that exactly six customers are very satisfied?B what is the probability that more than six customers are very satisfied?C. what is the probability that less than five customers are very satisfied?D. suppose that of seven customer selected, three responded that they are very satisfied. what conclusions can be drawn about the sample? the probability that three out of seven customers are very satisfied is__, assuming that 95% of customers are very satisfied. therefore, it is__that randomly selecting seven customers would result in three responding that they were very satisfied.(round all answers to four decimal places please)
Let X be the number of customers satisfied
Given:
Sample size (n) = 7
The probability that a customer is very satisfied = 0.95
The probability distribution function for a binomial distribution is:
[tex]P(X=x)=(^n_x)p^x(1-p)^{n-x}_{}[/tex](a) Probability that exactly 6 customers are satisfied
[tex]\begin{gathered} P(X=6)=(^7_6)(0.95)^6(1-0.95)^{7-6} \\ =\text{ 7}\times\text{ 0.7351}\times0.05 \\ =\text{ 0.25728} \\ \approx\text{ 0.2573} \end{gathered}[/tex]The probability that exactly six customers are very satisfied is 0.2
(b) Probability that more than 6 customers are very satisfied
Find the area of the circle with the diameter 8yd use the 3.14 for pie don’t round
Given:
a.) A circle with a diameter of 8 yards.
For us to get the area of the circle, we will be using the following formula:
[tex]\text{ Area = }\frac{\pi D^2}{4}[/tex]Where,
D = the diameter of the circle = 8 yards
We get,
[tex]\text{ Area = }\frac{\pi D^2}{4}[/tex][tex]\text{ = }\frac{(3.14)(8)^2}{4}[/tex][tex]\text{ = }\frac{(3.14)(64)}{4}[/tex][tex]\text{ = (3.14)(16)}[/tex][tex]\text{ Area = }50.24yd^2[/tex]Answer: 50.24 square yards
Translate the sentence into an equation.Seven less than the product of 6 and a number is 2.Use the variable x for the unknown number
Seven less than the product of 6 and a number is 2.
→ The product of 6 and a number can be expressed as 6x
→ "Seven less than the product of 6 and a number", indicates that you have to subtract 7 to 6x, so that: 6x-7
→ According to the sentence, the result of this calculation is seven, so the complete expression is:
[tex]6x-7=2[/tex]Stacy loaned Robert $21,370 at an interest rate of 10 % for 171 days. How much will Robert pay Stacy at the end of 171 days? Roundyour answer to the nearest cent. Note: Assume 365 days in a year and 30 days in a month.
The simple interest formula is :
[tex]A=P(1+rt)[/tex]where A is the future amount
P is the principal amount
r is the rate of interest
and
t is the time in years
From the problem, we have :
P = $21,370
r = 10% or 0.10
t = 171 days or 171/365 year
Using the formula above :
[tex]\begin{gathered} A=21370(1+0.10\times\frac{171}{365}) \\ A=22371.17 \end{gathered}[/tex]The answer is $22,371.17
Solve the following system of equations for all three variables.-8x – 3y + 5z = -2X-2y – 5z = -94x + 7y + 5z = 4
In order to solve this system of equations, first let's add the second equation to the first and third ones:
[tex]\begin{gathered} \begin{cases}-8x-3y+5z+(x-2y-5z)=-2+(-9) \\ 4x+7y+5z+(x-2y-5z)=4+(-9)\end{cases} \\ \begin{cases}-7x-5y=-11 \\ 5x+5y=-5\end{cases} \end{gathered}[/tex]Now, adding the two resulting equations, we have:
[tex]\begin{gathered} -7x-5y+(5x+5y)=-11+(-5) \\ -2x=-16 \\ x=8 \\ \\ 5x+5y=-5 \\ 40+5y=-5 \\ 5y=-45 \\ y=-9 \\ \\ x-2y-5z=-9 \\ 8+18-5z=-9 \\ -5z=-35 \\ z=7 \end{gathered}[/tex]So the solution for this system is x = 8, y = -9 and z = 7.
what is 5-2 squared plus 8/4=
Question:
what is 5-2 squared plus 8/4:
Solution:
Notice that:
[tex](5-2)^2+\frac{8}{4}\text{ = }3^2\text{ + 2 = 9 +2}=11[/tex]then, we can conclude that the correct answer is:
[tex]11[/tex]
Answer:
Step-by-step explanation:
1. 5-2=3
2. 8/4=2
3. (3x3)+2
4. 9+2
5. 11
ten years ago a man's age was 6 times the age of his son 12 years later the age of the Son will be 27 years what is the present age of his father
From this problem let's begin with some notation: Let the man age denoted by M. With the info provided we can do this:
Son age = 27-12= 15
Finally with the condition given we can createthe following equation:
[tex]M-10=6(15-10)[/tex]And solving for M we got:
[tex]M=6\cdot(5)+10=40[/tex]So then basically the answer for the men age is 40 years
At Tim Hortons, mike bought three coffees and 1 doughnut for $19. Bob bought one coffee and one doughnut for $9. Using the price of one coffee=c and the price of one doughnut=d . Answer the following questions 14,15,16 and 17
So first of all we need to write an algebraic equation for Mike. We know that he bought 3 coffees and 1 doughnut. Then the total price of these things is:
[tex]3c+1d=3c+d[/tex]And we know that he had to pay $19 so this expression is equal to 19:
[tex]3c+d=19[/tex]Then the answer to question 14 is the second option.
Bob bought one coffee and one doughnut so the total cost of his purchase is:
[tex]c+d[/tex]We know that this cost is equal to $9 so we get:
[tex]c+d=9[/tex]And the answer to question 15 is the third option.
In question2 16 and 17 we need to find c and d. For this purpose we need to use the algebraic equations for Mike and Bob:
[tex]\begin{gathered} 3c+d=19 \\ c+d=9 \end{gathered}[/tex]Let's take the second equation and substract c from both sides:
[tex]\begin{gathered} c+d-c=9-c \\ d=9-c \end{gathered}[/tex]Now we substitute this expression in place of d in the first equation:
[tex]\begin{gathered} 3c+d=3c+(9-c)=19 \\ 3c+9-c=19 \\ 2c+9=19 \end{gathered}[/tex]Now we substract 9 from both sides:
[tex]\begin{gathered} 2c+9-9=19-9 \\ 2c=10 \end{gathered}[/tex]And we divide both sides by 2:
[tex]\begin{gathered} \frac{2c}{2}=\frac{10}{2} \\ c=5 \end{gathered}[/tex]Then the price of one coffee is $5 so the answer to question 16 is the third option.
Now we are going to take the equation for Bob and take c=5:
[tex]c+d=5+d=9[/tex]If we substract 5 from both sides we get:
[tex]\begin{gathered} 5+d-5=9-5 \\ d=4 \end{gathered}[/tex]Then the price of one doughnut is $4 and the answer to question 17 is the second option.
evaluate each expression if x=6 x/2 +9
Answer
x = -27
Explanation
x = 6 (x/2 + 9)
x = 3x + 54
x - 3x = 54
-2x = 54
Divide both sides by -2
(-2x/-2) = (54/-2)
x = -27
Hope this Helps!!!
Suppose you pick a card out of a standard deck of 52 cards. What is the probability that you will choose a spade? Express your answer as a fraction.
hello
to solve this problem, we should understand that a standard deck of cards have 52 cards which consists of 13 spade.
the probability of choosing a spade is
[tex]\frac{13}{52}=\frac{1}{4}[/tex]the answer to this question is 1/4
I am trying to exercise but can’t do number 6
Subtract 2π to the given angle as it is equivalent to one revolution.
[tex]\begin{gathered} \frac{35\pi}{9}-2\pi \\ \frac{35\pi}{9}-\frac{18\pi}{9} \\ =\frac{17\pi}{9} \\ \\ \text{Subtracting further by }2\pi\text{ will result with coterminal angles outside the interval }(0,2\pi) \\ \\ \text{therefore, the coterminal angle of }\frac{35\pi}{9}\text{ in the interval }(0,2\pi)\text{ is } \\ \frac{17\pi}{9} \end{gathered}[/tex]2xsquare +17x-30Need to factor completelyAnswer is. (2x-3)(x+10)But, how to get to that answer????
Answer:
(2x-3)(x+10)
Explanation:
Given the expression 2x^2+17x-30, we are to factorize completely
2x^2+17x-30
= (2x^2+20x)-(3x-30)
Factor out the common terms
= 2x(x+10)-3(x+10)
= (2x-3)(x+10)
This gives the required factor
Can you find the correct answers to all parts of question 1 and 2. Could you also tell me why I got my answers wrong originally?
1.
Part a) G(x) is still a function because it's the inverse function of f(x).
part b)
f(g(4)).
FIrst step for this is to find g(4) which is:
[tex]\begin{gathered} g(4)=f^{\text{ -1}}(4) \\ \\ g(4)=f^{\text{ -1}}(4)=g(4)=3 \end{gathered}[/tex]Part c)
Now, to find the equation of the tangent line we have to find the slope, which is the derivative, because the derivative is the slope of the tangent line at a given x-value
But they ask for the g function, in this case:
[tex]\begin{gathered} f^{\text{ -1}}(\text{ -2\rparen} \\ then,\text{ g\lparen-2\rparen=7} \end{gathered}[/tex]So, the derivative in f(x)= 7 is -4.5
So, the equation is:
[tex]\begin{gathered} y\text{ - g\lparen-2\rparen=m\lparen x - \lparen-2\rparen} \\ y\text{ - 7= -4.5\lparen x+2\rparen} \\ \\ y\text{ - }7=\text{ -}4.5(x+2) \end{gathered}[/tex]