Gran is four times older than her grandson.their ages together total 75 years. a)how old is gran? b)how old will her grandson be in five years time?​

Answer:

-2, 1, 3

Step-by-step explanation:

Using elimination method, we get the result  630 + 630 + 35 = n

What is elimination method?

The elimination method involves removing one of the variables from a system of linear equations by adding or subtracting from the system and multiplying or dividing the variable coefficients.

You need an equation that can determine n, 630's total, and 35 more than 630.

More

The value "35 more in June than in May" refers to the value "35 more than 630." That value is represented by the sum (630 +35).

Total two months

In total, there will be two months' worth of delivered papers.

May deliveries + June deliveries = n

630 + (630 +35) = n

Eliminating parentheses, this expression is ...

630 + 630 + 35 = n

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Answer:

x = 8

measure of each side = 27 units

Step-by-step explanation:

Properties of an equilateral triangle:

If ΔGHJ is an equilateral triangle, the side measures are equal.

\(\implies \sf GH = HJ = GJ\)

\(\implies (5x-13)=(11x-61)=(7x-29)\)

To solve for x, choose 2 side lengths, equate them, and solve for x:

\(\implies \sf GH=HJ\)

\(\implies 5x-13=11x-61\)

\(\implies 5x-13 - 5x =11x-61 - 5x\)

\(\implies -13=6x-61\)

\(\implies -13+61=6x-61+61\)

\(\implies 48=6x\)

\(\implies 48 \div 6=6x \div 6\)

\(\implies x=8\)

To find the measure of each side, substitute the found value of x into one of the side expressions:

\(\begin{aligned}\implies \textsf{GH}&=5(8)-13\\& =40-13\\& =27\end{aligned}\)

Therefore, x = 8 and the measure of each side is 27 units.

Equilateral triangles have same sides

Length of each side

Answer:

9. The part of the equation that represents a quoient is (10÷2)  because inside the parentheses you solve the division equation and a quoitent is the answer to a division equation

10. The part of the expression that represents the product of two factors would be 6.7s because 6.7 is being multiplied by s, and a product is an answer to a multiplication problem

Step-by-step explanation:

9. The part of the equation that represents a quotient is (10÷2). 10.  The part of the equation that represents the product of two elements is 6.7s.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

6.7s - (10÷2) +15

9. The part of the equation that represents a quotient is (10÷2) since the division equation is solved inside the parenthesis and a quotient is the answer to a division problem.

10. Here 6.7 is multiplied by s, the component of the equation that represents the product of two elements is 6.7s, and a product is an answer to a multiplication expression.

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Answer:

5,4

Step-by-step explanation:

The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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Answer:

60

Step-by-step explanation:tanI=  

adjacent

opposite

​  

=  

3.8

6.7

​  

\tan I = \frac{6.7}{3.8}

tanI=  

3.8

6.7

​  

I=\tan^{-1}(\frac{6.7}{3.8})

I=tan  

−1

(  

3.8

6.7

​  

)

I=60.44\approx 60^{\circ}

I=60.44≈60  

∘

The smallest number that will make it divisible by 11 is n = 2 and the number is A = 7,01,69,302

Given data ,

Let the missing number be represented as n

Now , the value of the original number is A = 7,01,69,30*​

where * represents = n

To make a number divisible by 11, the difference between the sum of the digits in the odd-numbered positions and the sum of the digits in the even-numbered positions must be a multiple of 11.

On simplifying the equation , we get

To make the difference between the sums a multiple of 11, we need to add the smallest digit to the end. The smallest digit is 8

Hence , the number that is divisible by 11 is 7,01,69,302

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Answer:

30

Step-by-step explanation:

\(3*5*4=60\\\\\frac{60}{2} =30\)

Answer:

4 miles in 1 min

Step-by-step explanation:

The reasonable domain for the function is (b) x > 0

From the question, we have the following parameters that can be used in our computation:

The function f(x) = 75x + 100

Where x is the number of hours

f(x) is the total cost.

In this case, the number of hours cannot be negative or 0

This means that the values of x in the function would be x > 0

These values of x are the domain

So, the reasonable domain for the function os (b) x > 0

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Answer:

its a

Step-by-step explanation:

its a trust me

Answer:

y = x+5

Step-by-step explanation:

Answer:

\(y = x + 5\)

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

Lets say there's a line whose slope is 'm' & y-intercept is 'c'. So, the equation of line in slope-intercept form is → \(\boxed {y = mx + c}\)

SOLUTION :-

By using the basic idea of slope-intercept form , the equation of line given in the question is :-

\(y = (1 \times x) + 5\)

\(=> y = x + 5\)

x = -3 ==> 2(-3) + 1 = (-6) + 1 = -5

x = 9 ==> 2(9) + 1 = 18 + 1 = 19

x = 15 ==> 2(15) + 1 = 30 + 1 = 31

Answer:

18

Step-by-step explanation:

Change 3 into a fraction.

Which gives you 3/1

multiply 3/1 by the inverse of 1/6

3/1x1/6

Then you get 1 :)

Answer:

06 units

Step-by-step explanation:

Answer: -7x+4y-z would be the answer

Step-by-step explanation:

Answer:A.The triangles are similar but not congruent

Step-by-step explanation:

In a congruent traingle:

the both triangles are same in shape and size

There are five theorems to see if the triangles are congruent

and neither particularly applies here

sss: the sides are not equal

as none of the sides are equal, then despite the angles, congruence is not possible

However it is evident that one of the triangles is proportionally bigger than the other but similar. Hence A is correct.

Step-by-step explanation:

Answer:

1:2

Step-by-step explanation:1 out of the total 2 objects

Answer:

They each get 1 and 1/3 (one third). Do 4 (granola bars) divided by 3 (students) to get 1.33.

Answer:

Step-by-step explanation:

First, lets figure out which ones add up to 14

5+9=14

6+8=14

8+6=14

9+5=14

They all add up to 14.

Next, reverse the digits and see if it is 36 less than the original number

95 is not 36 less than 59

86 is not 36 less than 68

68 is only 18 less than 86

59 is 36 less than 95

So, the answer would be 95.

Answer:

x = y/(a + d).

Step-by-step explanation:

y = ax + dx

y = x(a + d)

Divide both sides by (a + d)

y / (a + d) = x

Answer:

y

x = --------------

a + d

Step-by-step explanation:

y = ax + dx

factorizing the equation above, we will get;

y = x ( a + d )

divide both sides of the equation by the co efficient of x which is (a + d)

therefor; y = x(a + d)

( a + d ) ( a + d )

we will then have ; x = y

a + d

Answer:

47 cm²

Step-by-step explanation:

3(9 - 4) + 8 × 4 = 15 + 32 = 47

Answer:

0

Step-by-step explanation:

x < 4 means all numbers less than 4, excluding 4 itself.

4.5 > 4.

5 > 4.

so 0 is the solution

Answer:

4

Step-by-step explanation:

interval notation ( negative infinity, 4)

Answer:

D stays for 1 and as B is -6

the length of BD should be 7

good luck <3!

Answer:

a. If the P-value is smaller than the significance level, the null hypothesis is rejected.

b. Pooled proportion = 0.8

c. z = 2.7

d. As the P-value (0.0072) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

We will use the P-value approach, so the decision rule is that if the P-value is lower than the significance level, the null hypothesis is rejected.

The claim is that the proportions differ significantly.

Then, the null and alternative hypothesis are:

\(H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0\)

The significance level is 0.05.

The sample 1, of size n1=200 has a proportion of p1=0.85.

\(p_1=X_1/n_1=170/200=0.85\)

The sample 2, of size n2=150 has a proportion of p2=0.7333.

\(p_2=X_2/n_2=110/150=0.7333\)

The difference between proportions is (p1-p2)=0.1167.

\(p_d=p_1-p_2=0.85-0.7333=0.1167\)

The pooled proportion, needed to calculate the standard error, is:

\(p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{170+110}{200+150}=\dfrac{280}{350}=0.8\)

The estimated standard error of the difference between means is computed using the formula:

\(s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.8*0.2}{200}+\dfrac{0.8*0.2}{150}}\\\\\\s_{p1-p2}=\sqrt{0.0008+0.00107}=\sqrt{0.00187}=0.0432\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.1167-0}{0.0432}=\dfrac{0.1167}{0.0432}=2.7\)

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

\(P-value=2\cdot P(z>2.7)=0.0072\)

As the P-value (0.0072) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

Answer:

6.871 decimeters

Step-by-step explanation:

687.1 square centimeters = 6.871 square decimeters

1 dm² = 100 cm²

Answer:

6.871

Step-by-step explanation:

calculator

Answer:

Step-by-step explanation:

Answer:

1 pound 3.4 ounces

Step-by-step explanation:

The distance you can travel on one gallon of gasoline is known as gas mileage. A new car's test drive covers 600 miles on 20 gallons of gas. 2250 miles are the unit rate.

Therefore,

600/20 = 30 miles/gallon

30mi/gal (75 gallons)

= 2250 miles

The complete question is:

Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 600 miles on 20 gallons of gas.

What is the unit rate? How far can you drive on 75 gallons of gas?

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