EXPLANATION
When x=6 and y=13 x+y = 6 + 13 = 19
x + y = 19
To find the height of a display in a museum, a person place a mirror on the ground 35ft from the display. Then he stepped back 5ft so he could see the top of the display. His eyes were about 5'4" from the ground. What is the height of the display?(ill send the image because it was to big)
Now let's calculate the angle of the first triangle. We will use the tangent function because we have information from the opposite side and the adjacent side.
[tex]\begin{gathered} \tan \theta=\frac{5\text{ ft 4''}}{5\text{ ft}} \\ \end{gathered}[/tex][tex]\begin{gathered} \theta=\tan ^{-1}(1.0666) \\ \theta=46.84\text{ degree} \end{gathered}[/tex]With this angle we can calculate the height of the display. Again we will use the tangent function.
[tex]\begin{gathered} \tan (46.84)=\frac{x}{35} \\ x=35\cdot\tan (46.84) \end{gathered}[/tex][tex]x=37.33\text{ ft}[/tex]The answer would be 37.33 ft the height of the display
5 2/5 × 0.8A. 4.32B. 5.76C.7.80D.2.75
Answer:
A. 4.32
Explanation:
First, we need to transform the mixed number 5 2/5 into a decimal number as:
[tex]5\frac{2}{5}=5+\frac{2}{5}=5+0.4=5.4[/tex]Then, we can multiply 5.4 by 0.8, so:
[tex]5\frac{2}{5}\times0.8=5.4\times0.8=4.32[/tex]To multiply 5.4 by 0.8, we can multiply the numbers normally without taking into account the decimal points. So 54 times 08 is equal to:
Then, 5.4 has one digit after the decimal point and 0.8 has one digit after the decimal point. So, in total, we have two digits after the decimal point. It means that the result is equal to 4.32 because we need two digits after the decimal point.
Therefore, the answer is 4.32
Round 6,752 to the nearest ten and nearest hundred.
Given the number:
6752
i) Round to the nearest ten:
To round to nearest ten means to rou
You are given the circumference of the circle and the measure of the central angle ACB. Find the length of arc AB.circumference = 36 feet; m ZACB= 40"The length of arc AB isfeet
the length of arc ACB is 4 ft
Explanation
the length of an arc is given by:
[tex]l=\frac{\theta}{360\text{ \degree}}2\text{ }\pi r[/tex]where l is the length or the arc, theta is the angle in degrees, r is the radius
so
Step 1
find the radius of the circle
[tex]\begin{gathered} 2\text{ }\pi r=36 \\ \text{divide boths ides by 2}\pi \\ \frac{2\text{ }\pi r}{2\text{ }\pi}=\frac{36}{2\pi} \\ r=\frac{18}{\pi} \end{gathered}[/tex]Step 2
now, replace in the formula
Let
angle= 40 °
[tex]\begin{gathered} l=\frac{\theta}{360\text{ \degree}}2\text{ }\pi r \\ l=\frac{40}{360\text{ \degree}}2\text{ }\pi(\frac{18}{\pi}) \\ L=\frac{40}{360}\cdot36 \\ l=4\text{ } \end{gathered}[/tex]therefore, the length of arc ACB is 4 ft
I hope this helps you
Given cos = 0.9528, find .
Given:
[tex]\cos \theta=0.9528[/tex]To find the value of θ,
[tex]\begin{gathered} \cos \theta=0.9528 \\ \theta=\cos ^{-1}(0.9528) \\ \theta=17.6739^{\circ} \end{gathered}[/tex]Order from Greatest to Least -2.30 , -13/4,-3 1/8,-14/5
According to the given data we have the following numbers:
-2.30 , -13/4,-31/8,-14/5
To order from Greatest to Least the above numbers first we would have to divide the numerator by the denominator of each of the fractions so we can get the decimal number and so it would be easier to order the numbers.
So:
-13/4=-3.25
-31/8=-3.875
-14/5=-2.8
Therefore, the Order from Greatest to Least of the numbers would be:
-2.30,-14/5,-13/4,-31/8
Your statistics class has 26 students in it - 14 girls and 12 boys. Your teacher uses a calculator to select two students at random to solve a problem on the board. Given that the second student chosen is a girl, what is the probability that the first student was also a girl?
The probability that the first student was also a girl is 0.175.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
The fraction of choosing a girl will be:
= Number of girls / Number of students
= 14 / 26
= 7/13
Therefore, the probability of having both girls will be:
= 7/16 × 6/15
= 0.175
The probability is 0.175.
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What is The percent increase of 78 to 124
The percent increase of 78 to 124 is: 58.97%
[tex]\frac{\text{ Final value }-\text{ Initial value}}{\text{ Initial value}}\cdot100=\frac{124-78}{78}=58.97\text{ \%}[/tex]rounded to the nearest percent is 59%
Simplify the expression:9m + 6( m + 7 )
ANSWER
15m + 42
EXPLANATION
We want to simplify:
9m + 6(m + 7)
To do this, first expand the bracket:
9m + 6m + 42
Now, collect like terms and simplify:
15m + 42
That is the simplified expression.
Solve the following exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 4^-x=2.6What is the exact answer? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set { } (simplify your answer. type an exact answer)B. There is no solution
Given:
[tex]4^{-x}=2.6[/tex]To solve for x:
Taking log on both sides
[tex]\begin{gathered} \log 4^{-x}=\log 2.6 \\ -x\log 4=\log 2.6 \\ -x=\frac{\log 2.6}{\log 4} \\ -x=0.689255811 \\ x=-0.689255811 \\ x\approx-0.689 \end{gathered}[/tex]Hence, the value of x is -0.689 (rounded to three decimal places).
describe the domain of the function f(x;y)= ln(4-x-y)
Domain of the given function is x∈(-2,∞)
Step-by-step explanation:
The given function is y=\ln(x+2)y=ln(x+2)
Domain is the set of x values for which the function is defined.
And we know that logarithm function is defined only for values greater than zero.
Therefore, for domain we have
x + 2 >0
x > -2
Hence, the domain of the
The domain of the function
f
(
x
,
y
)
=
ln
(
4
−
x
−
y
)
is the region of the x-y plane such that the argument of logarithm function is positive,...
See full answer below.
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What Is Domain and Range in a Function?
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Chapter 7 / Lesson 3
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What are the domain and range of a function? What are the domain and range of the graph of a function? In this lesson, learn the definition of domain and range as it applies to functions as well as how it applies to graphs of functions. Moreover, there will be several examples presented of domain and range and how to find them.
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Find f_x and f_y and graph f, f_x, and f_y with domains. f(x, y) = x^2y^3
А.
U. 3y2 +y-1
X-8
0.X-8+
G. X-3
+2x+1
D. 2k2+8k+15+
24
1. 3k +16 +-14
R X-1
Y. x2-3x +4 +
E. X+4
M. x2-8x +24 +-68
X+3
T. y2 – 8y +12
1 2 3
4 5
6 7
9
10
11
12
13 14
SOLUTION
After solving the numbers in front of the letters, we have:
A=4 ,B=14, C=2, D=6, E=1, F=15, G=17, H=27, I=33, J=3, K=40,L=22, M=5
N=19, O=11, P=16, Q=24, R=0, S=12, T=32, U=75, V=18, W=7, X=20, Y=35, Z=36
Now, we will match these numbers to the letters to form words.
4,16,0,33,22: APRIL
12,27,11,7,1,0,12: SHOWERS
5,4,35: MAY
15,22,11,7,1,0,12: FLOWERS
4,19,6: AND
1,18,1,0,35,32,27,33,19,17,12: EVERYTHING
33,19: IN
=● RATIOS, PROPORTIONS, AND PERCENTSFinding the principal, rate, or time of a simple interest loan or...Try AgainYour answer is incorrect.Alonzo borrowed $800 from a lender that charged simple interest at an annual rate of 9%. When Alonzo paid off the loan, he paid $216 in interest. How longwas the loan for, in years?If necessary, refer to the list of financial formulas. I need help with this math problem please.
The simple interest rate formula is:
[tex]A=P(1+rt)[/tex]To find the total amount We add:
[tex]A=800+216=1016[/tex]To find the total of years We can clear the t variable in the equation like this:
[tex]\begin{gathered} \frac{A}{P}-1=rt \\ \frac{\frac{A}{P}-1}{r}=t \end{gathered}[/tex]So We will find the time as follows:
[tex]t=\frac{\frac{1016}{800}-1}{0.09}=3[/tex]The loan was for 3 years.
Last year's freshman class at State University total 5,320 students. Of those 1,262 received a merit scholarship to help offset tuition costs. The amount a student received was N($3,450 , $480). if the cost of a full tuition was $4,050 last year , what percentage of students who received a merit scholarship did not receive enough to cover full tuition ? ( Round to nearest whole percent)Percentage of students ________%
Answer: We need to find the percentage of students that received a scholarship that did not cover their full tuition:
The number of students that received a scholarship was:
[tex]1262[/tex]The amounts that students received were:
[tex]\begin{gathered} 3,450\text{ Dollars} \\ 480\text{ Dollars} \end{gathered}[/tex]But the actual tuition cost was:
[tex]4050\text{ Dollars}[/tex]Therefore, none of the students that received scholarship had received enough to cover the full tuition, because:
[tex]\begin{gathered} 4050>3450 \\ 4050\text{ }>480 \end{gathered}[/tex]So, 100% of the students that received scholarships, did not receive enough to cover their tuition.
After watching some fish 40 feet below the surface of the water, a scuba diver went up 15 feet to explore a coral reef Use a number line to help you create an equation that shows the location of the coral reef in relation to the water's surface. mo Interpret the sum in the context of the problem A. The equation is -40 (-16) 28 The coral reef is 5 feet belo the water's surface
First he was 40 feet below surface, so he was at -40 feet
The he went up 15, so now he is -40 + 15 = -25, that means 25 feet below surface
So the right equation is D and for the line:
Victoria spends the two spinners shown 500 times solve a percent equation to predict the number of times the sum is less than or equal to 3. Enter the correct answers in the boxes.
Given t spinners :
The first has the numbers : from 1 to 5
The second has the numbers : from 1 to 3
So, the sum is less than or equal to 3 can get if the two spinners give 1 or 2
So, the probability to get 1 or 2 from the first spinner = 2/5
And the probability to get 1 or 2 from the second spinner = 2/3
So, total probability = 2/5 * 2/3 = 4/15 = 26.66%
She spends the two spinners 500 times
So, the equation will be :
[tex]26.66\%\times500=x[/tex]Solve for x:
[tex]26.66\%\times500=133.3[/tex]So, the number of times = 133
The tables of ordered pairs represent some points on the graphs of Lines F and G.
Line F
x y
2 7
4 10.5
7 15.75
11 22.75
Line G
x y
-3 4
-2 0
1 -12
4 -24
Which system of equations represents Lines F and G?
1. y=1.75x+3.5
y=-4x-8
2. same as 1 but -8 is -2
3. 1.75 and 3.5 are switched
4. 2 and 3 combined
The system of equation that represents lines F and G is (1) y = 1.75x + 3.5, y = -4x-8
To find the system of equation, we will put the values given tables in the equation given in the options.
For option (1)
y = 1.75x + 3.5 (For line F)
let's take the point (2,7) and put in the equation,
y = 1.75*2 + 3.5
= 3.5 +0.35
= 7
which is true.
Hence, (2,7) satisfies the equation.
y = -4x-8 (For line G)
lets take the point (-3,4) and put in the equation,
y = (-4)*(3) - 8
= 12 - 8
= 4
which is true.
Hence, (-3,4) satisfies the equation.
Therefore, Equation for line F is y = 1.75x + 3.5 and equation for line G is y = -4x-8.
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Jeremiah can drink 64 fluid ounces of coffee in 4 days. How many Quarts of coffee can he drink in 1 hour.help explain please:)
1 quart = 32 fluid ounces
Therefore, 64 fluid ounces = 2 quarts
Jeremiah can drink these 2 quarts in 4 days meaning he drinks
[tex]2\frac{\text{quarts}}{4\text{days }}=0.5\frac{\text{quarts}}{\text{days}}[/tex]Now, there are 24 hours in a day; therefore, the number of quarts Jeremiah drinks in 1 hour is
[tex]\frac{0.5\text{quarts}}{24\text{hours}}=\frac{1}{48}\frac{\text{quarts}}{\text{days}}[/tex]or in decimal form, this is 0.021 quarts in an hour.
Bob bought a $800 TV on sale for $650. What is the percent he saved?
Answer:
18.75%
Step-by-step explanation:
Since you want to know what percent he saved, first you have to figure out how much he saved.
800 - 650 = 150
Then to find the percent, find how much 150 is of 800.
[tex]\frac{150}{800} = 0.1875[/tex]
Since we're finding a percentage, multiply by a 100.
0.1875 × 100 = 18.75%
If it said to round, the answer would be 19%, but it doesn't, so keep it at 18.75%.
Ivan took out a loan for 6700 that charges an annual rate of 9.5% compounded quarterly. Answer each part.
We will have the following:
a) The amount after one year will be:
[tex]\begin{gathered} A=6700(1+\frac{0.095}{4})^{4\ast1}\Rightarrow A=7359.53647... \\ \\ \Rightarrow A\approx7359.54 \end{gathered}[/tex]So, the amount after 1 year will be approximately $7359.54.
b) The effective annual interest rate will be:
[tex]eair=(1+\frac{0.095}{4})^4-1\Rightarrow eair=0.0984382791...[/tex]So, the effective annual interest rate will be approximately 9.84%.
1 Lola collects blood donations at a clinic. 7/16 of the donations are of Type 0, 3/8 are of Type A, and 1/16 are Type AB. The remaining are Type B. What part of the blood donations are Type B?
Answer:
n=1/8
Explanation:
From the diagram, if we sum up all the parts, we have:
[tex]\frac{7}{16}+\frac{3}{8}+\frac{1}{16}+n=1[/tex]We solve the equation above for n.
The lowest common multiple of 16 and 8 = 16
Therefore:
[tex]\frac{7+6+1}{16}+n=1[/tex]Therefore:
[tex]\begin{gathered} \frac{14}{16}+n=1 \\ n=1-\frac{14}{16} \\ n=\frac{16-14}{16} \\ n=\frac{2}{16} \\ n=\frac{1}{8} \end{gathered}[/tex]The value of n is 1/8.
Given R(I, y) = (-y, z) and the point Qt1, 0), what is R(Q)?R(Q)
Given that R(x, y) = (-y, x)
This is a transformation.
We want to find R(Q)
The point Q is given as:
Q = (1, 0)
This means that x = 1 and y = 0
Therefore, for R(Q):
-y = -0 = 0
x = 1
Therefore:
R(Q) = (-y, x) = (0, 1)
which price below has the same unit rate as 3 cans for $ 1.98? Select All That Apply●6 cans for $4.00 ●5 cans for $5.90●2 cans for $1.32 ●4 cans for $3.60
Divide the price of 3 cans over 3 to find the unit rate:
[tex]\frac{1.98}{3}=0.66[/tex]Perform the same operation with the other rates to find which of them have the same unit rate:
6 cans for$4.00
[tex]\frac{4}{6}=0.67[/tex]5 cans for %5.90
[tex]\frac{5.90}{5}=1.18[/tex]2 cans for $1.32
[tex]\frac{1.32}{2}=0.66[/tex]4 cans for $3.60
[tex]\frac{3.60}{4}=0.9[/tex]Therefore, the only one which has the same rate as 3 cans for $1.98 is 2 cans for 1.32
In ∆QRS, q =370 cm, r =910 cm and
using cosine rule
[tex]\begin{gathered} s^2=r^2+q^2-2rq\cos S \\ s^2=910^2+370^2-2\times910\times370\cos 31 \\ s^2=828100+136900-336700\times0.8571673007 \\ s^2=965000-288608.230146 \\ s^2=676391.769854 \\ s=\sqrt[]{676391.769854} \\ s=822.430404262 \\ s=822\operatorname{cm} \end{gathered}[/tex]Find an equation for the perpendicular bisector of the line segment whose endpoints are (-2,1) and (-6,5)
Here, we want to find the equation of the perpendicular bisector of th line segment with the given endpoints
We start by calculating the slope of the line segment
Mathematically, we can have that as;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ m\text{ = }\frac{5-1}{-6-(-2)}=\text{ }\frac{4}{-4}\text{ = -1} \end{gathered}[/tex]So, we have the slope of the line as -1
Mathematically, the slopes of two lines which are perpendicular to each other have a product of -1
Thus;
[tex]\begin{gathered} m_2\text{ }\times\text{ (-1) = -1} \\ \\ m_2\text{ = 1} \end{gathered}[/tex]Now, we need the midpoint segment coordinates as it is the point through which the perpendicular bisector will pass through
We can get these coordinates using the mid-point formula
That will be;
[tex]\begin{gathered} (x,y)\text{ = (}\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}) \\ \\ (x,y)\text{ = (}\frac{-2-6}{2},\frac{1+5}{2}) \\ \\ (x,y)\text{ = (-4,3)} \end{gathered}[/tex]So we use the point-slope formula to get the equation
That will be;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3\text{ = 1(x+4)} \\ y-3\text{ = x + 4} \\ y\text{ = x + 4 + 3} \\ y\text{ = x + 7} \end{gathered}[/tex]you buy a new iphone 12 pro max for $1099 the value of the iphone decreases by 25% annually write a model for the value of the phone and use the model to see how much it would be worth after 3 years ?
The price of the iphone can be modeled by the following expression:
[tex]A=P(1-r)^t[/tex]where,
A: price of the iphone after t years
P: initial price = 1099
r: rate of percetage decrease in decimal for = 0.25
t: years
Then, the function becomes:
[tex]\begin{gathered} A=1099(1-0.25)^t \\ A=1099(0.75)^t \end{gathered}[/tex]The price of the iphone after t = 3 years, according to the previous expression is:
[tex]\begin{gathered} A=1099(0.75)^3 \\ A=463.64 \end{gathered}[/tex]Hence, the price of the iphone after 3 years would be $463.64
Maria drove 871 miles in 13 hrs. At the same rate, how many miles would she drive in 8 hours?
Given data: Distance= 871 and time =13 hrs
Required: Find the distance
Method: Find the speed first and then get the distance
Step 1: Find the average speed
[tex]\text{speed}=\frac{\text{distance covered}}{\text{time taken}}[/tex][tex]\text{speed}=\frac{871}{13}=67\text{ miles/hour}[/tex]Step 2: Find the distance to be covered in 8 hours
[tex]\text{Distance}=\text{ spe}ed\text{ x time taken}[/tex][tex]\begin{gathered} \text{Distance}=67\text{ miles/hour x 8 hours } \\ \text{Distance =536 miles} \end{gathered}[/tex]Therefore, Maria will drive 536 miles in 8 hours
Marisol wants to buy a backpack from the Gucci store. Gucci ishaving a sale of 45% off the regular price. If the regular price of aGucci backpack is $1375.23, then what will the new sale price beafter the discount of 45% is applied?
Regular price = $1375.23
Discount = 45% of Regular price
The discount = 45% of $1375.23
= 45/100 x $1375.23
= 0.45 x $1375.23
Discount = $ 618.85
But Sale price = Regular price - Discount
Sale price = $1375.23 - $618.85
Sale price = $756.38
Hence, the new sale price after the discount of 45% is applied is $756.38
The two shorter sides of a right triangle measure 18 ft and 24 ft. What is the measure in feet of the third side?
We have that in a right triangle, the larger side is the hypothenuse since the sum of the others angles must be equal to 90. Thus, we can apply the Pythagorean Theorem to solve this question.
The legs of the triangle are a = 18 ft, b = 24 ft, and c = ?.
Then, applying the Pythagorean Theorem, we have (without using units):
[tex]c^2=a^2+b^2\Rightarrow c^2=(18)^2+(24)^2\Rightarrow c^2=324+576\Rightarrow c^2=900[/tex]Then, taking the square root to both sides of the equation, we have:
[tex]\sqrt[]{c^2}=\sqrt[]{900}\Rightarrow c=30[/tex]Then, the measure of the third side (hypothenuse) is c = 30 ft.
Can someone help me with this math problem I have like 20 more and I really need help
We can find the x-intercept when y=0 so replacing y for 0 we have
[tex]\begin{gathered} -5x+2(0)=10 \\ -5x=10 \\ x=\frac{10}{-5}=-2 \end{gathered}[/tex]The x-intercept is (-2,0).
Now we are going to replace x for 0 to find the y-intercept
[tex]\begin{gathered} -5(0)+2y=10 \\ 2y=10 \\ y=\frac{10}{2}=5 \end{gathered}[/tex]The y-intercept is (0,5).
For the graph of 4x -9y=12 we have that the x-intercept is (3,0) and the y-intercept is (0,-4/3)