Answer:
1. 16
2. 36.62 in
Step-by-step explanation:
For the first one:
If you don't want to read the explanation go to the next section in bold
We are told that the triangles are similar.
We are told that the side lengths of the smaller triangle measure 7,4 and 9
And we are told that the longest side of the similar triangle measures 36
Given this information we need to find the other side lengths.
Because the triangles are similar each side length will share similar ratios. Note that the ratios must be between the two longest side, the two medium length sides and the two shorter sides
Because we are given the longest side length of the similar triangle and the longest side length of the smaller triangle we can set up a proportion to find the other side lengths.
The proportion can be found by dividing the longest side length of the larger triangle (36) by the longest side length of the smaller triangle (9)
proportion = [tex]\frac{36}{9} or4[/tex]
So the ratio to the side lengths of the triangle is 4 to 1
Now that we have created a proportion we can find the other side lengths.
Once again this information is not needed. If you don't want to read it go to the next section in bold.
For the medium length side: [tex]\frac{4}{1} =\frac{x}{7}[/tex] ( remember x = missing side length)
multiply each side by 7
4 * 7 = 28
x/7 * 7 = x
x = 28
For the shorter side: [tex]\frac{4}{1} =\frac{x}{4}[/tex] ( once again x = missing side length )
multiply each side by 4
4 * 4 = 16
x/4 * 4 = x
x = 16
So we can conclude that the side length of the shortest side is 16
For the second one
This problem is like the other one.
The only difference is we are already given the ratio
( note that the ratio is width to height )
16 : 9
Given the proportion and the height (20.6) of the other flat screen tv we need to find the width
To do so we set up an equation using the ratio:
let x = width
[tex]\frac{16}{9} =\frac{x}{20.6}[/tex]
using cross multiplication
16 * 20.6 = 329.6
9 * x = 9x now we have 9x = 329.6
step 2 divide each side by 9
9x / 9 = x
329.6/9 = 36.62
we're left with x = 36.62
Meaning that the width of the other flat screen tv is 36.62 in
In the following diagram,
ℓ
∥
m
.
Solve for each of the variables w, x, y, and z. For each solution, explain, in complete sentences which special angles allowed you to create an equation in order to find a solution.
Answer:
w = 94 degrees
x = 105 degrees
y = 75 degrees
z = 86 degrees
Step-by-step explanation:
The 75 degree angle + x = 180 degrees, because together they form straight line. They are supplementary angles.
180 - x = 75
x = 105 degrees
The 86 degree angle and z are equal, because they are vertical angles...they share a vertex. So z = 86 degrees
In some of the other problems we've looked at together, we've talked about corresponding angles. Angles in the same position on the next parallel line, cut by a transversal. The angle right above x, where p intersects l, corresponds to y. I've called it Y' in the picture I'm attaching.
So if the 75 degree angle is equal to its vertical angle, Y', which is equal to its corresponding angle of y. y = 75 degrees
Using all of what's here about supplementary angles and corresponding angles, you know that the two angles in the z/86 degree area are 94 degrees. (180 - 86 = 94) Which means w and its vertical angle are also 94 degrees. w = 94 degrees.
I'm sorry this is so wordy. I don't want it to be confusing for you. I am hoping I can help you understand enough so these problems don't stress you out :) I have circled vertical angle pairs (about half of them) in pink. I have circled the supplemental angle pairs (about half of them) in purple.
Label 1/4 on the number line. Label 1/2 on the number line .
Answer:
it goes 0 then 1/4 in the first notch 1/2 in the second notch 3/4 in the third notch then the number 1 on the fourth
Step-by-step explanation:
Hope that helps.
5 The table shows the linear relationship between the average height in feet of trees on a tree
farm and the number of years since the trees were planted.
Average Tree Height
Number of Years Since
1 3
the Trees Were Planted
6
11
15
Average Height (ft)
10
24
45
80
108
What is the rate of change of the average height in feet of the trees on the farm with respect
to the number of years since the trees were planted?
A 14 ft/yr
B 3 ft/yr
C 7 ftyr
D 10 ft/yr
Answer:7ft
Step-by-step explanation:
my final balance after 48 months was $869. If I originally put $800 into the bank what was the interest rate
Answer: 1.4375 percent
Step-by-step explanation:
69/48 = 1.4375 percent.
(if its incorrect I'm sorry)
Evaluate the following Piecewise Function.
Please sturggeling
Answer:
[tex]f(0)=4[/tex]
[tex]f(6) = 8[/tex]
Step-by-step explanation:
Given
The piece wise function
Solving (a): f(0)
To solve for f(0), we make use of:
[tex]f(x) = x + 4[/tex]
Because: the inequality [tex]x < 5[/tex] satisfies x = 0
i.e: [tex]0 < 5[/tex]
So, we have:
[tex]f(x) = x + 4[/tex]
[tex]f(0)=0 + 4[/tex]
[tex]f(0)=4[/tex]
Solving (b): f(6)
To solve for f(6), we make use of:
[tex]f(x) = 8[/tex]
Because: the inequality [tex]5 \le x < 7[/tex] satisfies x = 6
i.e: [tex]5 \le 6 < 7[/tex]
So, we have:
[tex]f(6) = 8[/tex]
Square has a perimeter of 76 Cm how long is each side?
simplify mentally 4867.293 ÷ 1000
Step-by-step explanation:
20htff5tgtgtgtgtf5ddrtfy g huhh
find the missing length
Answer:
36
Step-by-step explanation:
since the triangles are similar, that means that they have the same angles, and all 3 correlating sides have the same scaling factor.
C correlates to R.
B to Q.
A to P.
therefore,
CB correlates to RQ.
84 / 18 = 14 / 3
so, the scaling factor from ABC to PQR is
3/14
AB to PQ must have the same scaling factor :
168 × 3/14 = 12 × 3 = 36
which is also (of course) confirming the ratio of leg to baseline of the original triangle :
AB : CB = 168 : 84 = 2 : 1
and now
PQ : RQ = 36 : 18 = 2 : 1
Is urgent What is the equation of the line, in point-slope form, that goes through (2, -1)
and is perpendicular to y = 5x + 3?
A. Y+ 1 = 5(x - 2)
O B. y-1--5(x-2)
C. »+1-- *(x-2)
O D. v-2-- }(x+1)
Answer:
c. y + 1 = -⅕(x - 2)
Step-by-step explanation:
To write the equation in point-slope form, we need to know the slope (m) and coordinates of a point the line passes through.
The equation would be in the form of y - b = m(x - a).
(a, b) = (2, -1)
Since the line is perpendicular to y = 5x + 3, the slope will be the negative reciprocal of 5 which is -⅕
m = -⅕.
Substitute a = 2, b = -1, and m = -⅕ into y - b = m(x - a).
Thus:
y - (-1) = -⅕(x - 2)
y + 1 = -⅕(x - 2)
Hiuxian scores 68 out of 80 for her Science test, Priya scores 86 out of 120 for her Science test and Rui feng scores 120 out of 150 for his Science test. Who performs the best in his/her Science test?
Answer:
Hiuzian score the best in his/her science test.
Step-by-step explanation:
convert these fractions into percentage.
68/80 = 85%
86/120 = 71.67%
120/150 = 80%
Which statement best describes whether the function is linear or nonlinear?
Answer:
Is nonlinear because the common ratio is 3
Step-by-step explanation:
A linear function can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If this line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Now to this problem, if the data corresponds to a linear equation, then for any set of points we choose we should see the same slope.
For example, if we choose the first and second points:
(0,20) and (1, 60) the slope is:
a = (60 - 20)/(1 - 0) = 40/1 = 40
a = 40
Now if we choose the first and third points:
(0, 20) and (2, 180)
The slope is:
a = (180 - 20)/(2 - 0) = (160/2) = 80
So the slopes are different, which means that this function is nonlinear.
If we look at the f(x) values for the second point onwards, we can see that:
f(2) = 60
f(3) = 60*3 = 180
f(4) = 180*3 = 540
f(5) = 540*3 = 1620
and so on.
So this seems to be an exponential function with a common ratio of 3 between consecutive outputs.
Having a common ratio is not a property of linear functions, then the correct options is:
"Is nonlinear because the common ratio is 3"
A lifeguard is standing beside the lifeguard chair on a beach.The lifeguard is 76 inches tall and casts a shadow that is 48 inches long.The chair casts a shadow that is 72 inches long.How y'all is the lifeguard chair?
9514 1404 393
Answer:
114 inches, or 9 ft 6 inches
Step-by-step explanation:
The chair's shadow is 72/48 = 1.5 times as long as the lifeguard's shadow. Since shadow length is presumed proportional to height, we expect the lifeguard chair to be 1.5 times as tall as the lifeguard.
1.5(76 in) = 114 in = 9 ft 6 in . . . height of lifeguard chair
Resuelve lo siguiente:
1.-Carlos tiene un mazo de 15 cartas numeradas del 1 al 15. Saca una carta al
azar, ve el número, y la revuelve de nuevo en el mazo. ¿Cuál es la probabilidad de
que no le salga una carta menor o igual a 5 en el primer intento, pero que si le
salga una carta menor o igual a 5 en el segundo intento?
1
1
2
B) 9
A) 9
C) 3
D) 3
Respuesta:
2/9
Explicación paso a paso:
Dado que :
tarjeta numerada = 1 - 15
Probabilidad de obtener un número no menor o igual a 5
Número de cartas no menor o igual a 5:
Tarjeta no ≤ 5 = (6,7,8,9,10,11,12,13,14,15) = 10
Probabilidad = resultado requerido / Total de resultados posibles
P (Tarjeta no ≤ 5) = 10/15 = 2/3
Número de cartas menor o igual a 5:
Tarjetas ≤ 5 = 1, 2, 3, 4, 5
P (Tarjeta ≤ 5) = 5/15 = 1/3
P (Tarjeta no ≤ 5) * P (Tarjeta ≤ 5)
2/3 * 1/3 = 2/9
Calcularemos la probabilidad del evento combinado para obtener: P = 0.22
Calculando las probabilidades individuales:La probabilidad de sacar una carta menor o igual a 5 es igual al cociente entre el numero de cartas con un número menor o igual a 5 y el número total de cartas en el mazo.
Tenemos 5 cartas con un número igual o menor a 5 y un total de 15 cartas, así que la probabilidad es:
p = 5/15
La probabilidad de que no le salga una carta menor o igual a 5 es calculada de la misma forma, hay 10 cartas que no son menores o iguales a 5 y un total de 15 cartas, entonces tenemos:
q = 10/15
La probabilidad conjunta es simplemente el producto de esas dos probabilidades, así obtenemos:
P = (10/15)*(5/15) = 10/45 = 0.22
Sí quieres aprender más sobre probabilidad, puedes leer:
https://brainly.com/question/21755457
Find the volume of a right circular cone that has a height of 5.1 ft and a base with a diameter of 15.4 ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
V = 419.459168
Step-by-step explanation:
hope this helps
9514 1404 393
Answer:
316.7 ft³
Step-by-step explanation:
The formula for the volume of a cone is ...
V = 1/3πr²h
Here, the radius (r) is half the diameter, so is 7.7 ft. Then the volume is ...
V = 1/3π(7.7 ft)²(5.1 ft) = 100.793π ft³ ≈ 316.6505 ft³
The volume of the cone is about 316.7 cubic feet.
_____
If you use the inappropriate value 3.14 for π, your answer will be 316.5 ft³.
I need to increase the numbers of customers I talk to daily by 20% how many customers do I need to talk to if I talk to a average of 8 customers per hour during an 8 hour shift
Answer:
77 approx
Step-by-step explanation:
Given data
Number of customers talked to per hour= 8
Hence for 8 hours(a day) the number of customers talked to = 8*8= 64
We want to first find 20% of 64
=20/100*64
=0.2*64
=12.8
Hence the number of customers will be
=12.8+64
=76.8
=77 approx
Marvin earns $9.75 per hour at his summer job. He wants to buy a video game system that costs $263.25
Enter an equation to model the relationship between the number of hours worked h and the amount earned e
The equation is:
Answer:
$9.75h=e-$263.25
Step-by-step explanation:
-15x + 5 = -10x + 25 solve for x
Answer:
Move all terms containing x to the left side of the equation.
−5x+5=25
Move all terms not containing x to the right side of the equation.
−5x=20
Divide each term by −5 and simplify.
x=−4
Step-by-step explanation:
Answer:
[tex]15x + 5 = -10x + 25[/tex]
[tex]15x+5-5=-10x+25-5[/tex]
[tex]15x=-10x+20[/tex]
[tex]15x+10x=-10x+20+10x[/tex]
[tex]25x=20[/tex]
[tex]\frac{25x}{25}=\frac{20}{25}[/tex]
[tex]x=\frac{4}{5}[/tex]
what order pair is 3 up and 2 to the right of point t
15
12
П
[Not drawn to scale)
What is the area of the reduced rectangle?
Paul is buying packages of hot dogs for a camping trip. Each package is 30 oz. If he buys 4 packages, about how many pounds of hot dogs is he buying?
Answer:
7.5 OR 8 (Depending on whether you are rounding or not)
Step-by-step explanation:
30 x 4 = 120 oz
120 oz to pounds is 7.5 but if you are rounding then its 8.
In a pet shop, there are 3 hamsters for every 2 guinea pigs, and there are 2 giant cloud rats for every 3 guinea pigs. If N is the total number of hamsters, guinea pigs, and giant cloud rats, and N>0 then what is the smallest possible value of N
Answer:
n = 19.
Step-by-step explanation:
If there are x guinea pigs then there are 3/2 x and 2/3 x rats.
So n = x + 3/2 x + 2/3 x
n = 19x / 6
19x = 6n
Let x = 6 , then n = 19*6 / 6 = 19.
Now n and x must be whole numbers so x is 6 and n = 19 are the smallest possible values.
on a twelve hours clock the time is quarter -past nine. where does the long head and point ?
Answer:
It points to 3 in on the clock.
Hope it helps!!!
Use <, >, or = to compare the following decimals.
(a) 6.37 |?| 2.68
(b) 0.1 |?| 0.04
(0) 7.7 |?| 7.70
Answer:
A is >
B is >
C is =
I hope this helps you.
a rectangle has a length of 18 ft less than 7 times its width if the area of the rectangle is 405 square feet. what's the length of the rectangle
Answer:
i don't know um is there any multiple questions?
Step-by-step explanation:
How many times does the pyramid fit in the cube of both bases and height are the same?
plz help first right gets brainly
Answer:
D, see attachment
Step-by-step explanation:
An equation with a squared symbol (²) will never be linear. You can also graph these lines to be sure.
The attachment shows each of these graphed.
Red line- A
Orange line- B
Green line- C
Purple line- D
Line D is nonlinear, so the answer is D.
Select all the properties of a right triangle.
A. Has a right angle
B. Has one obtuse angle
C. Has parallel lines
D. Has perpendicular lines
E. Has three acute angles
help pleasee no links!!
What is the rate of change of the function y - 6x + 3?
Answer:
6
i think the - was meant to be an = instead of -
Step-by-step explanation:
rate of change is the same as slope
that is slope-intercept form.
y=mx+b
m is slope
slope= 6
Answer:
The rate of change is 6
Step-by-step explanation:
Set the equation equal to 0:
y-6x+3=0
Now solve for y because we want the equation in y=mx+b form where m is the rate
Subtract 3:
y-6x=-3
add 6x
y=6x-3
Now in y=mx+b form
m would equal 6
1. 80% of the students on a field trip love the movie. If there are a total of 50 students on the field trip, how many love the movie?
Answer:
40 students
Step-by-step explanation:
A helpful tip I use is x% of y= y% of x
For example, 50% of 80 is 40
Boom
Which of the following is not a solution of the equation y=3x−4 ?
(2, 2)
(0, -4)
(4, 8)
(-1, -1)
Answer:
(-1, -1) is not a solution to the system
Step-by-step explanation:
Y = 3x - 4. Substitute the points for x and y
2 = 3(2) - 4
2 = 2 solution
y = 3x - 4
-4 = 3(0) - 4
-4 = -4 solution
y = 3x - 4
8 = 3(4) - 4
8 = 8 solution
y = 3x - 4
-1 = 3(-1) - 4
-1 = -7 not solution