Answer:
SS: $3,602.20
M: $842.45
Step-by-step explanation:
58100 x 0.062 = 3,602.2
58100 x 0.0145 = 842.45
Area of a Circle Ji-Min needs to replace a circular window having a diameter of 5 ft. She decides to use double strength glass costing $ 3 per square foot. Find the total cost for the glass.
Ji-Min will spend a total of $235.62 to fence or cover the area of the circular window.
Area of a CircleWhat is the area of the a circle?
The area of circle is equal to pi times square of its radius, i.e. πr². To find the area of circle we have to know the radius or diameter of the circle.
Let's find the area of the circle first;
radius = diameter / 2
radius = 5 / 2
radius = 2.5ft
The area of the circle is;
A = πr²
A = π * 5²
A = 25π
A = 78.54ft²
For every square foot, the glass cost $3, this implies that 3 * 78.54 will be the total cost to cover the window.
cost = 3 * 78.54 = $235.62
She will spend $235.62 to fence the window
Learn more on area of circle here;
https://brainly.com/question/24375372
#SPJ1
If she decides to use double strength glass costing $ 3 per square foot. the total cost for the glass is $58.88.
How to find the total cost?Given data:
Diameter = 5ft
Glass costing = $3 per square foot
Hence,
Let the radius be 5/2 feet
Area = π × (5/2)²
Area = 25π /4 ft²
So,
Total cost = ( π × 25 /4 × $3)
Total cost = $58.875
Total cost = $58.88
Therefore $58.88 is the total cost.
Learn more about total cost here:https://brainly.com/question/5168855
#SPJ1
Use the graph of y=h'(x) below, to estimate point(s) of inflection for the function h(x) , as
well as the intervals on which h(x) is concave up and concave down. Explain your reasoning.
Answer:
At x = 0 and at x = 2 there are points of inflections. In the intervals of
(negative infinity, 0) and (2, positive infinity) it is concave up.
In the intervals of (0, 2) it is concave down.
Step-by-step explanation:
Inflection points are point where h'(x) changes from increasing to decreasing and vise versa.
When a graph is concave up, h'(x) is increasing.
When a graph is concave down, h'(x) is decreasing.
1. Mark is going to a carnival. He is anxiously looking forward to riding as many rides as possible. In order to enter the park each person is charged a $3 admission fee. The tickets for the rides are $0.75 each.
Match the following number of rides (x) and the total cost with admission (y) for Mark's trip to the carnival for 0 to 4 rides.
1 --> $3.00
2 --> $4.50
4 --> $3.75
3 --> $6.00
0 --> $5. 25
2. Write an equation that describes the relationship between the number of rides (x) and the total cost (y).
3. Use your equation from question #2, to determine the cost of 100 tickets.
4. If Mark's grandmother gave him $50, how many rides could be ridden? (no decimals)
Answer: hi
Step-by-step explanation:
this is it
the product of two and a number, divided by five 5
The expression of the given statement is [tex]\frac{2x}{5}[/tex] .
What is algebraic expression?
When terms are combined using operations like addition, subtraction, multiplication, division, etc., the result is an algebraic expression (or variable expression). Let's look at the formula 5x + 7 as an illustration. Consequently, we can state that 5x + 7 is an illustration of an algebraic statement. Here are some more examples: 5x + 4y + 10
Here the given product of two and a number. Lets us take number as x. Then ,
=> 2*x= 2x
Product of two and a number divided by 5. Then,
=> [tex]\frac{2x}{5}[/tex]
Hence the algebraic expression of the given statement is [tex]\frac{2x}{5}[/tex] .
To learn more about algebraic expression refer the below link
https://brainly.com/question/4344214
#SPJ1
Please help I was sick and missed out on class.Thank you
Answer:
slope = (1/3)
Step-by-step explanation:
(-8, 2), (-11, 3)
(x₁, y₁) (x₂, y₂)
m = slope
y₂ - y₁ 3 - 2 1 1
m = ------------ = -------------- = ----------- = -------
x₂ - x₁ -11 - (-8) -11 + 8 3
I hope this helps!
Justin is designing a drink container in the shape of a rectangular prism.
The container must be made out of 254 cm² of plastic.
Will the container be large enough to hold 1 cup of liquid? Justify your answer.
(1 cup = 236 cm³)
The container is large enough to hold 1 cup of liquid.
Will the container be large enough?From the information, Justin is designing a drink container in the shape of a rectangular prism and the container must be made out of 254 cm² of plastic.
In this case, since 1 cup = 236cm², it can be seen that 254cm² is more than 236cm².
Therefore, the container is large enough.
Learn more about liquid on:
brainly.com/question/752663
#SPJ1
What are the zeros of the function f(x)=x²-x² - 2?
O +3, ti
O +2, ti
O +√2 ti
O+√3, ti
The zeros of the function f(x) = x⁴− x² − 2 are ±√2 or x = ±i option third positive or negative square root of 2, ±i is correct.
What is a complex number?
It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a function:
f(x) = x⁴− x² − 2
Assume u = x²
f(x) = u² - u - 2
(u + 1)(u - 2)
(x² + 1)(x² - 2)
x² = -1
x = √1
x² = 2
x = √2
x = ±√2 or x² = -1 ⇒ x = ±i
Thus, the zeros of the function f(x) = x⁴− x² − 2 are ±√2 or x = ±i option third positive or negative square root of 2, ±i is correct.
Learn more about the complex number here:
brainly.com/question/10251853
#SPJ1
How many cubic inches are in an aluminum can with a 2 3/5 diameter and 5 1/4 in height?
According to the volume of cylinder formula, an aluminum can with a 2 3/5 diameter and 5 1/4 in height are in 27.86 cubic inches.
Volume of Cylinder
The formula to calculate the volume of the cylinder is
Volume of a cylinder = πr²h cubic units.
where
r refers the radius
h refers the height.
Given,
Here we have an aluminum can with a 2 3/5 diameter and 5 1/4 in height and now we have to find the volume in cubic inches.
While we looking into the given question, we know the following values,
Diameter = 2 3/5
When we simplify it, then we get the value of diameter as
d = 13/5 or 2.6
Similarly, the value of height is rewritten as,
h = 5.25
So, based on the formula of volume of cylinder,
We get the value as,
=> V = π x (2.6/2)² x 5.25
Apply the value of π as 3.14, then we get,
=> V = 3.14 x (1.3)² x 5.25
=> V = 16.485 x 1.69
Therefore, the volume in cubic inches is 27.86 cubic inches.
To know more about Volume of cylinder here.
https://brainly.com/question/17106541
#SPJ1
find the slope of (-4,4) (0,0)
The slope for the following question is = 4.
What is slope?Slope is used to describe the steepness of a line. The definition of slope is the rise of a line over the run of a line, or the change in the vertical direction (y) over the change in the horizontal direction (x). When one thinks of skiing down a hill or climbing up a mountain, the angle at which they are descending or ascending is the slope. Sometimes the slope can be fairly flat or very steep depending on what it is.The slope of an object indicates how steep it is. Slope knowledge is crucial for daily decision-making. For instance, understanding a roof's slope enables builders to determine whether specific construction materials are required for shingling projects. Since there must be sufficient grade for water to pass through the tile, slope is crucial in agriculture when tiling a field. Slope can also be calculated using elevation points on a GIS, a type of digital map that can highlight areas with sharp elevation changes in the ground.acc to our question-
the two y's are 0 and 4 so its 0-4then the two x's are0 and one so its 0-10-4/0-1 is -4/-1 which when simplified the negatives cancel out leaving you with a positive 4hence the value of slope=4
learn more about slope click here:
https://brainly.com/question/3493733
#SPJ1
Lisa wants to buy a hat that costs 114 Argentine Pesos.She has $25.Does she have enough money to buy the hat?
Answer:
150
Step-by-step explanation:
I had this on one of my quizzes, hope this helps :D
if ally worked 20.56 hours , and makes $10 an hour . how much is pay check? show work.
Answer:
$205.6
Step-by-step explanation:
20.56hours × $10/hour = $205.6
A college football game is played to a sell-out crowd of 20,500 people. Student tickets are $7 while general admission tickets are $12. A
total of $176,000 was collected from ticket sales. How many people purchased student tickets? How many people purchased general
admission tickets?
people purchased student tickets and people purchased general admission tickets.
14000 student tickets and 6500 general admission tickets were purchased during the football game
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers.
Let x represent the amount of students tickets and y represent the amount of general admission tickets.
A total of $176,000 was collected from ticket sales. Hence:
7x + 12y = 176000 (1)
A college football game is played to a sell-out crowd of 20,500 people. Hence:
x + y = 20500 (2)
From the two equations:
x = 14000, y = 6500
14000 student tickets and 6500 general admission tickets
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
An assistant is in charge of ordering lunch for the monthly office meeting. For the first month, she orders five Falafel wraps, fifteen Turkey BLT sandwiches, and twenty hot Ham and Swiss paninis for a total of $260. The next month, she orders eight Falafel wraps, eighteen Turkey BLT sandwiches, and 14 hot Ham and Swiss paninis for a total of $263. For the third month, she orders twelve Falafel wraps, 16 Turkey BLT sandwiches, and twelve hot Ham and Swiss paninis for a total of $258. How much does each sandwich cost?
The cost of Falafel wraps is $5.5, the cost of Turkey BLT sandwiches is $7.5, and the cost of hot Ham and Swiss paninis is $6.
How much does each sandwich cost?In order to determine the cost of each sandwich, we would assign variables to the cost of sandwiches ordered, and then translate the word problem into algebraic expression as follows:
Let the variable f represent the cost of Falafel wraps.Let the variable t represent the cost of Turkey BLT sandwiches. Let the variable h represent the cost of hot Ham and Swiss paninis.Therefore, translating the word problem into an algebraic expression, we have the following;
For the first month ⇒ 5f + 15t + 20h = 260 ......equation 1.
The next month ⇒ 8f + 18t + 14h = 263 ......equation 2.
For the third month ⇒ 12f + 16t + 12h = 258 ......equation 3.
Next, we would solve the system of algebraic expressions simultaneously.
Multiplying equation 1 by 12/5 and subtracting it from equation 3, we have:
6.25t - 24h = -366 ......equation 4.
Multiplying equation 2 by 5/8 and subtracting it from equation 1, we have:
3.75t + 11.25h = 95.625 ......equation 5.
Solving equation 4 and equation 5, we have:
Falafel wraps, f = $5.5
Turkey BLT sandwiches, t = $7.5
Hot Ham and Swiss paninis, h = $6.
Read more on cost of Falafel wraps sandwiches here: https://brainly.com/question/15936179
#SPJ1
X-y=3 determine the x and y intercepts of linear equations
Answer:
y-intercept (0,-3)
x-intercept (3,0)
Step-by-step explanation:
Let x = 0
-y =3
y = -3
(0,-3)
Let y = 0
x = 3
(3,0)
Last week, Lisa sold 20 hand-engraved watch bands, earning a total profit of $105.00. She plans to make 50 engraved watch bands to sell at the community art fair. If she sells all 50 watch bands, how much profit can Lisa expect to earn?
$
Answer:
$262.50
Step-by-step explanation:
20 : 105 = 50 : x
x = (50 * 105)/20
x = (5 * 105)/2
x = 525/2
x = 262.50
Answer: $262.50
Step-by-step explanation:
What I did was divide the $105 by 20 and got $5.25. I then multiplied $5.25 by 50 since that's how many she's going to sell and got $262.50.
Determine which set of side measurements could be used to form a right triangle.
square root of 18, square root of 32, 50
square root of 14, 6, square root of 50
4, 8, 20
4, 5, 6
The set of side measurements that could be used to form a right triangle is
square root of 14, 6, square root of 50How to determine the side measurements that could be used to form a right triangleThis gotten by Pythagoras theorem, with the formula stated as
hypotenuse² = opposite² + adjacent²
plugging the values as in the problem
50² = (√18)² + (√32)²
50² = 18 + 32
50² = 50 - incorrect
(√50)² = 6² + (√14)²
50 = 36 + 14
50 = 50 - correct
20² = 8² + 4²
400 = 64 + 16
400 = 80 - incorrect
6² = 5² + 4²
36 = 25 + 16
36 = 41 - incorrect
Learn more on Pythagoras theorem here:
https://brainly.com/question/29241066
#SPJ1
Simplify: (x^5) ^5?
Answer:
x^25
Step-by-step explanation:
The simplified expression is x²⁵.
Given is an expression (x⁵)⁵, we need to simplify the expression.
To simplify the expression (x⁵)⁵, we need to apply the exponentiation rules.
The exponent outside the parentheses should be distributed to each term inside the parentheses.
In this case, the exponent outside is 5, and the term inside the parentheses is x⁵.
To distribute the exponent, we multiply the exponents together.
Applying the rule, we get:
(x⁵)⁵ = x⁵⁽⁵⁾ = x²⁵
Therefore, the simplified expression is x²⁵.
Learn more about expression click;
https://brainly.com/question/28170201
#SPJ6
What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
x^2+32+116=12x
Answer:
Below
Step-by-step explanation:
x^2 + 32 + 116 = 12x 1st intermediate step: put everything on one side
x^2 -12x + 148 = 0 2nd intermediate step : re-arrange with constant on R
x^2 -12x = -148 3 rd intermediate step : take 1/2 of the 'x' coefficient
square it and add to both sides
x^2 -12x + 36 = -148 + 36 4th intermediate step : simplify
(x-6)^2 = -112
QUESTION 1 1 POINT
Jason bought new shoes priced at $75 and sales tax is 6%. What is the total cost of the shoes after-tax?
Provide your answer below:
The total cost of the shoe after tax is $79.50
Calculating total cost after sales taxFrom the question, we are to determine the total cost of the shoes after tax.
From the given information,
Jason bought new shoes priced at $75
and
The sales tax is 6%
The total cost of the shoe = Price of the shoe + Sales tax
Sales tax = 6% of $75
Sales tax = 0.06 × $75
Sales tax = $4.50
Thus,
Total cost of the shoe = $75 + $4.50
Total cost of the shoe = $79.50
Hence, the total cost is $79.50
Learn more on Calculating total cost after sales tax here: https://brainly.com/question/13283182
#SPJ1
At a livestock market, one customer purchased 4 sheep and 2 cows for a total of $1660. Another customer purchased 3 sheep and 5 cows for a total of $2925. Create a system of equations and solve it with substitution or elimination, and find the price of a sheep, and the price of a cow.
Answer:
[tex]s \approx \$182.14[/tex]
[tex]c \approx \$435.72[/tex]
Step-by-step explanation:
Set up a system of equations, where s is the cost of a sheep and c is the cost of a cow:
[tex]4s + 2c = \$ 1660[/tex], [tex]3s + 5c = \$ 2925[/tex]
First, isolate c in the first equation.
[tex]4s + 2c = \$ 1660[/tex]
[tex]2c = \$ 1660 - 4s[/tex]
[tex]c = \$ 840 - 2s[/tex]
Next, substitute this value into the second equation:
[tex]3s + 5c = \$2925[/tex]
[tex]3s + 5(\$840 - 2s) = \$2925[/tex]
and simplify.
[tex]3s + \$4200 - 10s = \$2925[/tex]
[tex]-7s = -\$1275[/tex]
[tex]7s = \$1275[/tex]
[tex]s \approx \$182.14[/tex]
Finally, plug this value into the first equation to get the value of c:
[tex]4(\$182.14) + 2c = \$1660[/tex]
[tex]2c = \$1600 - \$728.57[/tex]
[tex]c \approx \$435.72[/tex]
So, a sheep costs about $184.14, and a cow costs about $435.72.
6. Use words and numbers to explain how the number 0.4 can mean 40/100 and 4/10 at the same time
Answer:They are all the same because 40/100 divided by 10 on both sides is just 4/10 and 4/10 as a decimal is equal to 0.4
Step-by-step explanation:
Answer:
0.4 is the decimal form of [tex]\frac{4}{10}[/tex], which means that 4 ÷ 10 = 0.4, shown below.
If you multiply the numerator and denominator of [tex]\frac{4}{10}[/tex] by 10, you would get [tex]\frac{4*10}{10*10} =\frac{40}{100}[/tex]. This is equal in value to [tex]\frac{4}{10}[/tex] because 40 ÷ 100 = 0.4.
Find the equation for a polynomial f(x) that satisfies
▪ Degree 5
▪ Root of multiplicity 2 at x =
= -4
▪ Root of multiplicity 1 at x = -1
■ Root of multiplicity 2 at x = -2
▪y-intercept of (0, 128)
The polynomial function that has the degree of 5 is written as f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128
Polynomial function:
The equations formed with variables, exponents and coefficients are known as the polynomial equations. And it can have different exponents, where the higher one is called the degree of the equation.
Given,
Here we have the following things,
Degree = 5
Root of multiplicity 2 is x = -4
Root of multiplicity 1 at x = -1
Root of multiplicity 2 at x = -2
y-intercept of (0, 128)
Here we need to find the polynomial equation of the function.
According to the given roots of multiplicity, we have the factors of the polynomials are,
=> (x + 4)² (x + 1) (x + 2)²
So, the general form of the polynomial function can be written as,
=> f(x) = A (x + 4)² (x + 1) (x + 2)²
In order to find the 5 degree polynomial function, we have to calculate the value of A.
To Find the value of A, we have to apply the y - intercept point on the equation then we get,
=> 128 = A (0 + 4)² (0 + 1) (0 + 2)²
=> 128 = A (4)² (1) (2)²
=> 128 = A (16 x 1 x 4)
=> 128 = 64A
=> A = 2
Now, the polynomial function is written as,
=> f(x) = 2 (x + 4)² (x + 1) (x + 2)²
When we expand this one then we get,
=> f(x) =2 [x⁵ + 13x⁴ + 64x³ + 148x² + 160x + 64]
Therefore, the resulting polynomial function is,
=> f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128
To know more about Polynomial function here.
https://brainly.com/question/12914312
#SPJ1
A. x² +5
B. +5X
C.X + 5
D.5X
The expression that represents the quotient of given model is x + 5
The correct answer is an option (C)
In this question, we have been given a synthetic division of x^2 + 5x and x
We need to find the quotient.
x + 1 + 1 + 1 + 1 + 1
x) x^2 x x x x x
- x^2
0 x
- x
0 x
- x
0 x
- x
0 x
- x
0 x
- x
0
Therefore, the expression that represents the quotient of given model is x + 5
The correct answer is an option (C)
Learn more about an expression here:
https://brainly.com/question/1859113
#SPJ1
What’s the answer by chance
The sales tax rate of the cocktail table is 0.055
What is sales tax ?A sales tax is a consumption tax imposed by the government on the sale of goods and services
The cocktail table sold for $250 and the sales tax amount was $13.75. The sales tax rate can be calculated as follows:
Sales tax = list price * sales tax rate
Therefore,
sale tax rate = sales tax / list price
sales tax = $13.75
list price = $250
sale tax rate = 13.75 / 250
sales tax rate = 0.055
learn more on sale tax here:https://brainly.com/question/858105
#SPJ1
Solve the problem below
Answer:
f(-2) = 2
Step-by-step explanation:
-2 is the input/ domain value
It's corresponding value from the graph is 2.
Solve the equation for V.
P = IV
Enter the value that belongs in the
green box.
V
v = 8
The value of of V in the equation is P / I.
How to make a variable the subject of the formula?The equation given is P = IV and we were asked to solve for V. This means we should make V the subject of the formula in the equation.
The subject of a formula is the variable which is expressed in terms of the other variables.
Therefore, we have to express V in terms of other variables.
Hence,
P = IV
divide both sides by I
[tex]\frac{P}{I} = \frac{IV}{I}[/tex]
Hence,
V = p / I
learn more on equation here: https://brainly.com/question/28919888
#SPJ1
Which fractions have a LCD of 84?
100 Point's 50 points each have a blessed day
The fractions have a LCD of 84 is option C, 2/21,1/4,1/3.
Given:
3/14,1/42,1/6
= 3/14 + 1/42 + 1/6
= 9+42+7 / 42
The LCD is 42 not 84.
2/84,1/16,1/42
= 6+21+8 / 336
The LCD is 336 not 84
2/21,1/4,1/3
= 8+21+28 / 84
The LCD is 84
2/3,1/6,1/7
= 28+7+6 / 42
The LCD is 42 not 84
Therefore the fractions have a LCD of 84 is option C, 2/21,1/4,1/3.
Learn more about the LCD here:
https://brainly.com/question/21345138
#SPJ1
Answer:
[tex]\textsf{C)} \quad \dfrac{2}{21}, \dfrac{1}{4}, \dfrac{1}{3}[/tex]
Step-by-step explanation:
The least common denominator (LCD) is the smallest number that is exactly divisible by each denominator of a set of fractions.
To find the LCD of a set of fractions, reduce the fractions to their smallest equivalent, list the multiples of each denominator, then locate the smallest common number.
[tex]\textsf{A)} \quad \dfrac{3}{14}, \dfrac{1}{42}, \dfrac{1}{6}[/tex]
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, ...
Multiples of 42: 42, 84, 126, 168, 210, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Therefore, the LCD is 42.
[tex]\textsf{B)} \quad \dfrac{2}{84}, \dfrac{1}{16}, \dfrac{1}{42}=\dfrac{1}{42}, \dfrac{1}{16}, \dfrac{1}{42}[/tex]
Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, ... , 336, ...
Therefore, the LCD is 336.
[tex]\textsf{C)} \quad \dfrac{2}{21}, \dfrac{1}{4}, \dfrac{1}{3}[/tex]
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ... , 84, 88, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ... , 84, 87, ...
Therefore, the LCD is 84.
[tex]\textsf{D)} \quad \dfrac{2}{3}, \dfrac{1}{6}, \dfrac{1}{7}[/tex]
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ... , 42, 45, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, ...
Therefore, the LCD is 42.
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −43, ordered pair: (0,−25)
Answer:
[tex] \huge{ \bold{y = - 43x - 25}}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is given by
[tex]y = mx + c[/tex]
where
m is the slope
c is the y intercept
From the question
m = - 43
In order to find c we substitute the point (0,−25) into the equation y = mx + c
That's
[tex] - 25 = - 43(0) + c \\ - 25 = 0 + c \\ c = - 25[/tex]
We now substitute m and c into the equation
We have the final answer as
[tex] \bold{y = - 43x - 25}[/tex]
Hope this helps you
cannot decide which of two washing machines to buy. The selling price of each is $550. The first is marked down by 40%. The second is marked down by 30% with an additional 10% off. Find the sale price of each washing machine. Use pencil and paper. Explain why should buy the first washing machine rather than the second if the machines are the same except for the selling price.
The selling price of the two washing machies are
first washing machine is $330second washing machine is $346.5I will buy the first because it has a lower selling price
How to determine the best washing machine to buyThe question is a percentage problem
The first washing machine has a mark down by 40%
= 40 percent
= 40 / 100
= 0.4
marked down factor = 1 - 0.4 = 0.6
selling price of the first machine = 550 * 0.6 = 330
the second washing machine has mark down of 30%
30% = 0.3
marked down factor = 1 - 0.3 = 0.7
selling price of the second washing machine at first mark down
= 550 * 0.7 = 385
marked down again
10% = 0.1
the factor here is = 1 - 0.1 = 0.9
selling price of the second washing machine at second mark down
= 385 * 0.9 = 346.5
Learn more about percent here:
https://brainly.com/question/29325921
#SPJ1
can someone help with this
Answer:
z=38
Step-by-step explanation:
Using the fact that angles on a straight line add to 180°, the interior angles of the triangle are 86°, (180-3z)°, and (180-4z)°.
Angles in a triangle add to 180°, so:
[tex]86+180-3z+180-4z=180 \\ \\ 86-3z+180-4z=0 \\ \\ 266-7z=0 \\ \\ 7z=266 \\ \\ z=38[/tex]