The expression ab means that a is multiplying b.
Substituting with a = 2/7 and b = 2/5 into the expression we get:
[tex]\frac{2}{7}\cdot\frac{2}{5}=\frac{2\cdot2}{7\cdot5}=\frac{4}{35}[/tex]Spencer went to the county fair and spent his money only on ride tickets and fair admission. He bought 17 tickets for the rides and spent a total of $30.75 at a county fair. The county fair charges $1.25 per ticket for the rides and the price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets. (a) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission. (b) Explain your answer to Part 1a.
The linear equation y = 1.25x + 9.5 can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Spencer bought 17 tickets for the rides and spent a total of $30.75 at a county fair.
Let x be the number of tickets and y be the total cost:
Total ticket cost = 17×1.25 = $21.25
Admission fari = 30.75 - 21.25 = $9.5
The linear equation is:
y = 1.25x + 9.5
Here 9.5 represents the fixed admission fair.
Thus, the linear equation y = 1.25x + 9.5 can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
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Using compatible numbers to estimate, which expression has a quotient of about 70?
O A. 3,424 ÷ 49
OB. 5,358 ÷ 89
O C. 6,409 ÷ 79
O D. 5,238 ÷ 89
Brainliest. Find x and length
Value of x is 4 and length of QR is 15cm.
Define parallelograms.A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees. A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal. The illustration displays a parallelogram ABCD with the coordinates AB II CD and AD II BC. Moreover, AB = CD and AD = BC. Non-Example: A parallelogram is not represented by a trapezium.
Given Data
In rectangle, two parallel line are equal.
PS = -1+ 4x
QR = 3x +3
So,
Value of x will be:
-1 + 4x = 3x +3
4x - 3x = 3 +1
x = 4
For length of QR,
3x +3
3(4) +3
12 +3
15
Value of x is 4 and length of QR is 15cm.
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which statements are true about points A,B, and C check all that applyA. the coordinates of point a are (3, -3)B. the coordinates of point B (1, -3)C. the coordinates of Point C are (-2,2)D. Point C is the closest to the Y axisE. points A and B are the same distance from the y-axisIk the pic is blurry sorry
By the graph, we can see that the only statement that apply is B. the coordinates of point B is (1, -3).
The Morgans bought a $333,000 condominium. They made a down payment of $47,000 and took out a mortgage for the rest. Over the course of 30 years theymade monthly payments of $1714.72 on their mortgage until it was paid off.(a)(b)What was the total amount they ended up paying for the condominium(including the down payment and monthly payments)?$1]How much interest did they pay on the mortgage?I need help with this math problem.
Given: The following on the purchase of a Condominium
[tex]\begin{gathered} Price(Condominium)=333000 \\ Down-payment=47000 \\ Monthly-payment=1714.72 \\ Time=30years \end{gathered}[/tex]To Determine: The total amount they ended up paying for the condominium
Solution
Please note that we have 12 months in a year. The total number of months in 30 years would be
[tex]\begin{gathered} 1year=12months \\ 30years=30\times12months \\ 3oyears=360months \end{gathered}[/tex]Total monthly payments would be
[tex]\begin{gathered} 1month=1714.72 \\ 360months=360\times1714.72=617299.20 \end{gathered}[/tex]Therefore, the total amount they ended up paying for the condominium would be the addition of the down payment and the monthly payments
[tex]Total-amount(Paid)=47000+617299.20=664299.20[/tex]Hence, the total amount they ended paying for the condominium is $664,299.20
The interest paid on the mortgage would be the difference between the total amount paid and the cost
[tex]\begin{gathered} Interest=(Total-amount-paid)-Cost(condominium) \\ =664299.2-333000 \\ =331299.20 \end{gathered}[/tex]Hence, the interest paid on the Mortgage is $331,299.20
y= -5x+2 (Function rule)
The complete table using function rule y = -5x+2 is:
x y
-2 12
0 2
2 -8
4 -18
What is a function rule for a table?A function table includes a function rule as well as input and output values. If we plug in various values for the input, we obtain corresponding values of output according to the function rule. The relationship between the input values x and the output values y always follows a pattern that is specified by the function rule.Given:
Function rule, y = -5x+2.
We have to find the values of y by substituting different values of x.
When,
x = -2
y = -5(-2) + 2 = 10+2 = 12
x = 0
y = -5(0) + 2 = 0+2 = 2
x = 2
y = -5(2) + 2 = -10+2 = -8
x = 4
y = -5(4) + 2 = -20+2 = -18
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Which of the following inequalities is false?
A: 10 < 9 incorrect answer
B: 9 < 10 incorrect answer
C: 10 > 9 incorrect answer
D: 9 (is less than or equal to)
The inequalities 9 < 10 incorrect answer and 10 > 9 incorrect answer are false. Option (B) and Option (C) are false.
Before we determine the false statement, we must understand that all negative values are less than positive values and all positive values are greater than negative values,
For the inequality 10 < 9 incorrect answer
Since, it is given that 10 is less than 9 is incorrect answer and we know that 10 is greater than 9 . Therefore, this inequality is true.
For the inequality 9 < 10 incorrect answer
Since, it is given that 9 is less than 10 is incorrect answer but we know that 9 is less than 10. Therefore, this inequality is false.
For the inequality 10 > 9 incorrect answer
Since, it is given that 10 is greater than 9 is incorrect answer but we know that 10 is greater than 9 . Therefore, this inequality is false.
For the inequality 9 (is less than or equal to) 10 incorrect answer
Since, it is given that 9 (is less than or equal to) 10 is incorrect answer and we know that 9 is less than 10. Therefore, this inequality is true.
Therefore, Option (B) and Option (C) are false.
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While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 25 degrees. After walking 350 ft closer, he guessed that the angle of elevation had increased by 14 degrees. Approximately how tall is the hill?A. 475 feetB. 385 feetC. 608 feetD. 202 feet
The line sketch of the movement and positioning of Joe and the hill are shown below.
Brief description of the sketch made.
From the sketch, point A is where Joe started from heading towards the hill.
The hill is represented by BC and the height is h
25 degrees was the initial angle of elevation.
After moving 350 ft closer to the hill, the angle of elevation increased by 14 degrees to 25 + 14 = 39 degrees.
From triangle BCD,
Using the trigonometric function of tan,
[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 39=\frac{h}{x} \\ 0.8098=\frac{h}{x} \\ \text{Making h subject of the formula,} \\ h=0.8098x \end{gathered}[/tex]From triangle ABC,
Using the trigonometric function of tan,
[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 25=\frac{h}{350+x} \\ \text{Substituting the value of h gotten from the previous triangle,} \\ \tan 25=\frac{0.8098x}{350+x} \\ 0.4663=\frac{0.8098x}{350+x} \\ C\text{ ross multiplying,} \\ 0.4663(350+x)=0.8098x \\ 163.205+0.4663x=0.8098x \\ C\text{ ollecting the like terms,} \\ 163.205=0.8098x-0.4663x \\ 163.205=0.3435x \\ \text{Dividing both sides by 0.3435 to get x,} \\ x=\frac{163.205}{0.3435} \\ x=475.124ft \\ \\ \text{The height, h of the hill is;} \\ h=0.8098x \\ h=0.8098\times475.124 \\ h=384.755ft \\ h\approx385ft \end{gathered}[/tex]Therefore, the height of the hill is 385 feet
The correct answer is option B.
Find the minimum and maximum values of the function on the interval [11,27].
Can someone give examples of negative exponents in the world
Eg : seize of bacteria 1*10^-4
The example of negative exponent in the real world is the world's smallest bat, the bumblebee bat weighs of 7 × 10^-2 ounces
How to illustrate the information?An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite.
The multiplicative inverse of the base raised to a power with the opposite sign of the provided power is referred to as a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. The bat has a negative exponent.
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I would like to this math sentence question that I will send a picture of
Let
x -----> number of hours
we have that
the inequality that represents this situation is
[tex]45-12t\ge9[/tex]solve for t
[tex]\begin{gathered} -12t\ge9-45 \\ -12t\ge-36 \\ t\leq3 \end{gathered}[/tex]that means
the bakery can sell bread for a timeless than or equal to 3 hours
A line passes through (5,-4) and (-1,-4). Write the equation of the line in slope-intercept form.
Explanation:
The formula of the slope of a line that passes through points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]For this problem the slope is:
[tex]m=\frac{-4-(-4)}{5-(-1)}=\frac{-4+4}{5+1}=\frac{0}{6}=0[/tex]A slope of zero indicates that the line is horizontal. Therefore it is a constant.
The slope-intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept. In this case, the slope is zero so we just have:
[tex]y=b[/tex]b is the y-coordinate of the given points: b = -4
Answer:
y = -4
a1.Find the equation for a polynomial f(x) that satisfies the following:Degree 5Root of multiplicity 1 at x = 3• Root of multiplicity 2 at x = 2• Root of multiplicity 2 at x = -3y-intercept of (0, -216)f(x) =
we have that
the polynomial is of the form
f(x)=a(x-3)(x-2)^2(x+3)^2
where
a is the leading coefficient
y-intercept -----> (0,-216)
For x=0
substitute and solve for a
-216=a(0-3)(0-2)^2)(0+3)^2
-216=a(-3)(-2)^2(3)^2
-216=a(-3)(4)(9)
-216=-108a
a=2
therefore
[tex]f(x)=2(x-3)(x-2)^2(x+3)^2[/tex]If the links in a 30-inch necklace each measure three-eights of an inch long, how many links would be in then necklace?
ANSWER
80 links
EXPLANATION
To find how many links would be in the necklace, we have to divide the total length of the necklace, 30 inches, by the length of each link, 3/8 inch,
[tex]30\div\frac{3}{8}[/tex]Use the KCF method:
• K,eep the first fraction
,• C,hange the division sign into a multiplication sign
,• F,lip the second fraction,
[tex]30\div\frac{3}{8}=30\times\frac{8}{3}[/tex]30 and 3 can be simplified - 30 is 3 times 10,
[tex]30\times\frac{8}{3}=10\times8=80[/tex]Hence, the necklace would have 80 links.
Calculate each value requested for the following set of scores.a. ΣΧ=b. ΣΧ2=c. (ΣΧ)2=d. SS=Scores: 2, 3, 0,5Round to the hundredths place.
a.
[tex]\Sigma x=2+3+0+5=5+5=10[/tex]b.
[tex]\Sigma x^2=2^2+3^2+0^2+5^2=4+9+25=38[/tex]c.
[tex](\Sigma x)^2=(2+3+0+5)^2=10^2=100[/tex]d.
[tex]\begin{gathered} SS=\Sigma(x-\bar{x})^2 \\ where: \\ \bar{x}=\frac{2+3+0+5}{4}=\frac{10}{4}=2.5 \\ so: \\ SS=(2-2.5)^2+(3-2.5)^2+(0-2.5)^2+(5-2.5)^2 \\ SS=(-0.5)^2+(0.5)^2+(-2.5)^2+(2.5)^2 \\ SS=13 \end{gathered}[/tex]A recipe called for the ratio of sugar to flour to be 4:1 if you used 28 ounces of sugar how many ounces of flower would you need to use
Using ratios we can conclude that we need 7 ounces of flour.
What is the ratio?When the second number in the ordered pair, b, is not equal to 0, the ratio is written as a/b. An equation in which two ratios are made equal is known as a proportion. As an illustration, you could write the ratio as 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. The proportions of oranges to the total amount of fruit are 8:14 for oranges and 6:8 for lemons, respectively.So, ounces of flour need:
The ratio of sugar to flour is 4:1.The sugar used is 28 ounces.Then calculate for flour as follows:
4:1 = 28:x4/1 = 28/x4x = 28x = 28/4x = 7
Therefore, using ratios we can conclude that we need 7 ounces of flour.
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please help
A bird flying over water drops a crab from a height of 10 feet. The distance
the crab is from the water as it falls can be represented by d in the equation
d equals negative t to the power of 2 end exponent plus 10, where t is time in seconds. To catch the crab as it falls, a different
bird flies along a path represented by the equation d equals 5 t plus 5. In how many
seconds will the second bird catch the crab before it hits the water?
Solving a quadratic equation we can see that the second bird catches the crab after 0.85 seconds.
In how many seconds the second bird catches the crab?
The equation that describes the height of the crab is:
d = -t^2 + 10
The equation that represents the path of the second bird is:
d' = 5t + 5
The bird will be able to catch the crab when both are at the same height, this happens when:
-t^2 + 10 = 5t + 5
We need to solve this for t.
-t^2 + 10 - 5t - 5 = 0
-t^2 - 5t + 5 = 0
Using the quadratic formula we will get:
t = (5 ± √( (-5)^2 - 4*(-1)*5))/(2*-1)
t = (5 ± 6.7)/(-2)
We only care for the positive solution, which is:
t = (5 - 6.7)/(-2) = 0.85
So the bird catches the crab after 0.85 seconds.
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write a function to describe the following scenario.a basketball player practices jump shots. she starts at zero points and scores 5 points per minute. how many points will she have scored after a certain number of minutes?Y = ?x
number of minutes : x
number of points scored after x minutes : y
points scored per minute : 5
y=5x
multiply the points scored per minute (5) by the number of minutes (x). The expression is equal to the total number of points scored (y).
need help with this problem drop down 1, 2 dashed, soliddrop down 3 4 below, above
The boundary line is graphed as a dashed line if the symbols < or > are used, and as a solid line if the symbols ≥ or ≤ are used.
For an inequality in slope-intercept form, the half-plane above the line is shaded if the symbols > or ≥ are used, and the half-plane or ≤ are used. the line is shaded if the symbols < or ≤ are used.
Find the value of w and YZ if Y is between X and Z
w = 4 and YZ=24
1) XY = 4w
YZ= 6w
XZ=12w-8
2) Let's draw this to better understand it
So using the Segment Addition Postulate principle, let's write and solve
12w-8 =4w+6w
12w-8=10w
12w-10w -8=10w-10w
2w-8=0
2w-8+8=8
2w=8
w=4
3) The value for YZ =
6w => 6(4) YZ =24
-4x + 0.4y = -0.8 6x + 0.4y = 4.2 The solution to the system is ( , ).
An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign, as in 3x+5=11. A number that may be entered for the variable to produce a true number statement is the answer to an equation.
Explain about the solution?An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Take into account the formula 7x - 35 = 0. If we solve, we get either x = 5 or 7x = 35. The following linear equation only has one solution, x = 5, because the above linear equation is only true if x = 5.
The solution to this system (x=0.5 y=3)
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identify which value is not in the domain of the piecewise function
From the graph we notice that the only value of x for which the fuction generating the graph it not defined is x=-3.
Answer: A).
Simplify.
[3 (4-2)] x (16-4x3)
O 10
O 24
O 360
O 468
hope that help s you soooooooooooooooooo much
3x=8y-34y+2x=5Based on the system of equations above, what is the value of x/y?
To solve the given system of equations, we can solve the first equation for x, then we combine the equations
[tex]\begin{gathered} 3x=8y-3 \\ x=\frac{8y-3}{3} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 4y+2x=5 \\ 4y+2(\frac{8y-3}{3})=5 \\ 4y+\frac{16y-6}{3}=5 \\ 4y+\frac{16}{3}y-2=5 \\ \frac{12y+16y}{3}=5+2 \\ \frac{28y}{3}=7 \\ 28y=7\cdot3 \\ y=\frac{21}{28} \\ y=\frac{3}{4} \end{gathered}[/tex]So, y = 21/28.
Now, we use the y-value to find x.
[tex]\begin{gathered} x=\frac{8\cdot\frac{21}{28}-3}{3}=\frac{\frac{168}{28}-3}{3}=\frac{\frac{84}{14}-3}{3}=\frac{\frac{42}{7}-3}{3} \\ x=\frac{\frac{42-21}{7}}{3}=\frac{\frac{21}{7}}{3}=\frac{3}{3}=1 \end{gathered}[/tex]Hence, the value of each variable is x = 1 and y = 3/4.Use the properties of logarithms to write the following expression as a single term that doesn't contain a logarithm.e6-8ln(x)+In(y)
Given:
The expression is,
[tex]e^{6-8\ln (x)+\ln (y)}[/tex]Explanation:
Simplify the expression by using logathimic properties.
[tex]\begin{gathered} e^{6-8\ln (x)+\ln (y)_{}}=e^{6-\ln (x^8)+\ln (y)} \\ =e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)} \end{gathered}[/tex]Simplify further.
[tex]\begin{gathered} e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)}=e^6\cdot\frac{1}{e^{\ln(x^8)}}\cdot e^{\ln (y)} \\ =e^6\cdot\frac{1}{x^8}\cdot y \\ =\frac{e^6y}{x^8} \end{gathered}[/tex]So answer is,
[tex]\frac{e^6y}{x^8}[/tex]clasificar el siguiente polinomio2xy +9b -4z + 9
Los polinomios se clasifican según el número de términos que lo componen.
Los términos de una expresión están separados entre sí por los signos "+" y "-"
Se conoce como "monomio" a un polinomio con un solo término.
Son ejemplos de monomios:
6x²
2x
z
Un "binomio" es un polinomio de dos terminos.
Por ejemplo:
2x-3y
4x²+1
5y⁴z-2x²
Un "trinomio" es un polinomio con tres términos.
Por ejemplo:
2x+3y+z
y²-z+7
Un "cuadrimonio" es un polinomio de cuatro términos
Por ejemplo
xy+5y-9z+4
Los polinomios también pueden clasificarse según su grado. El grado del polinomio está dado por el valor del mayor exponente.
Un polinomio de grado cero es aquel que tiene coefficientes igual a cero.
Por ejemplo
0x²+0x
Un polinomio de primmer grado es aquel en el que la variable está elevada a la uno. En general este exponente no se escribe por lo que en un polinomio grado uno las variables no van a tener exponente.
Por ejemplo
x+2
x+y+4
Un polinomio de segundo grado es aquel cuyo mayor exponente es dos, es decir, tiene un termino elevado al cuadrado.
Por ejemplo:
x²
x+y²+3
x-9y+5z²-7
Un polinomio de tercer grado es aquel cuyo mayor exponente es tres, es decir, al menos una variable está elevada al cubo.
Por ejemplo:
x
x³+y²
2x-y³+25
Teniendo estas definiciones en cuenta, puedes clasificar el polinomio:
[tex]2xy+9b-4x+9[/tex]Este polinomio tiene 4 términos, "2xy", "9b", "4x" y "9" por lo que se lo puede clasificar como un cuadrimonio.
Como puedes ver, ninguna de las variables tiene exponente, es decir que, el exponente de mayor valor es 1, por lo que se puede clasificar como un polinomio de primer grado.
Entonces esta expresión es un cuadrimonio de primer grado
Solve the equation:2.5t=20
In order to solve this equation for t, we just need to divide both sides of the equation by 2.5.
So we have that:
[tex]\begin{gathered} 2.5t=20 \\ \frac{2.5t}{2.5}=\frac{20}{2.5} \\ t=\frac{20}{2.5} \\ t=8 \end{gathered}[/tex]So the solution for this equation is t = 8.
Rick and Chumlee buy and sell sports collectibles. Rick bought 14 rookie cards and 13 autographed baseballs
for a total of 263 dollars. Chumlee bought 17 cards and 4 baseballs for a total of 284 dollars. Let c be the cost
of each card and let b be the cost of an autographed baseball.
a) Write an equation relating the items bought by Rick:
b) Write an equation relating the items bought by Chumlee:
c) Solve the system above using substitution and interpret in context:
The cost of a card is
dollars.
dollars and the cost of a baseball is
a) equation relating the items bought by Rick is
14c + 13 b = 263
b)equation relating the items bought by Chumlee
17c + 4b = 284
C) The cost of a card is 16
The cost of a baseball is 3
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical truths. It takes variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a meaningful mathematical statement. All branches of mathematics, including coordinate geometry, calculus, and trigonometry, employ algebra. A fundamental algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations like addition, subtraction, multiplication, division, etc. are done on variables and constants.
Rick and Chumlee buy and sell sports collectibles.
Let c be the cost of each card and let b be the cost of an autographed baseball.
Rick bought 14 rookie cards and 13 autographed baseballs
for a total of 263 dollars.
a) equation relating the items bought by Rick is
14c + 13 b = 263
Chumlee bought 17 cards and 4 baseballs for a total of 284 dollars.
b)equation relating the items bought by Chumlee
17c + 4b = 284
C)
14c + 13 b = 263 .....(i)
17c + 4b = 284......(ii)
[tex]b = \frac{284-17c}{4}[/tex]
put the value of b in equation 1 you will get
14c +13([tex]\frac{284 - 17c}{4}[/tex])=263
56c + 3692 - 221c = 1052
175c = 2640
c = 16
[tex]b = \frac{284-17c}{4}[/tex].....(iii)
put the value of c in equation 3
b = [tex]\frac{284 - 17(16)}{4}\\ = \frac{12}{4}[/tex]
= 3
The cost of a card is 16
The cost of a baseball is 3
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A student must have an average (the mean) on five tests that is greater than or equal to 80% but less than 90% to receive a final grade of B. Devon’s grades on the first four tests were 76%, 65%, 89%, and 80%. What range of grades on the fifth test would him a B in the course? ( Assume that 100% is the highest grade possible.)
Enter the range of grades necessary for Devon to earn a b average.
__% < x < 100%
- -
Answer:
90% ≤ x ≤ 100%Step-by-step explanation:
Test results are:
76, 65, 89, 80 and x.The average of 5 tests should be:
80 ≤ average < 90, to get a B.The average is:
(76 + 65 + 89 + 80 + x)/5 = (310 + x)/5Plug it into inequality:
80 ≤ (310 + x)/5 < 90 Multiply by 5400 ≤ 310 + x < 450 Subtract 31090 ≤ x < 140But the maximum possible result from one test is 100%, considering this top score Devon must get:
90% ≤ x ≤ 100%Solve the inequality and express your answer in intervalvenation use decimal form for numeric values
Given:
[tex]\frac{20}{4}<\frac{z+7}{2}<\frac{25}{4}[/tex]Required :
To solve this
Explanation:
[tex]\begin{gathered} first\text{ of all separate compound inequalities into system of inequalities} \\ \\ \frac{z+7}{2}>\frac{20}{4}\text{ }\frac{z+7}{2}<\frac{25}{4} \\ \\ reduce\text{ the fraction} \\ \\ \frac{z+7}{2}>5\text{ or z+7>2}\times5 \\ \\ z+7>10 \\ \\ z>10-7 \\ \\ z>3 \end{gathered}[/tex][tex]\begin{gathered} \frac{z+7}{2}<\frac{25}{4} \\ \\ multiply\text{ both sides of the inequality by the least common denominator} \\ \\ 4\times\frac{z+7}{2}<4\times\frac{25}{4} \\ \\ reduce\text{ the expression to the lowest term} \\ \\ 2(z+7)<25 \\ \\ 2z+14<25 \\ \\ 2z<25-14 \\ \\ z<\frac{11}{2} \end{gathered}[/tex][tex]\begin{gathered} z>3\text{ and z <}\frac{11}{2} \\ \\ 3Required answer:3
